Kirchhoff’s theorem for Prym varieties
We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel–Prym map. In pa...
Gespeichert in:
| Veröffentlicht in: | Forum of Mathematics, Sigma Jg. 10 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, UK
Cambridge University Press
01.01.2022
|
| Schlagworte: | |
| ISSN: | 2050-5094, 2050-5094 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel–Prym map. In particular, we show that the map is harmonic, determine its degree at every cell of the decomposition and prove that its global degree is
$2^{g-1}$
. Along the way, we use the Ihara zeta function to provide a new proof of the analogous result for finite graphs. As a counterpart, the appendix by Sebastian Casalaina-Martin shows that the degree of the algebraic Abel–Prym map is
$2^{g-1}$
as well. |
|---|---|
| AbstractList | We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel–Prym map. In particular, we show that the map is harmonic, determine its degree at every cell of the decomposition and prove that its global degree is
$2^{g-1}$
. Along the way, we use the Ihara zeta function to provide a new proof of the analogous result for finite graphs. As a counterpart, the appendix by Sebastian Casalaina-Martin shows that the degree of the algebraic Abel–Prym map is
$2^{g-1}$
as well. We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a semi-canonical decomposition of the tropical Prym variety, via a careful study of the tropical Abel–Prym map. In particular, we show that the map is harmonic, determine its degree at every cell of the decomposition and prove that its global degree is $2^{g-1}$. Along the way, we use the Ihara zeta function to provide a new proof of the analogous result for finite graphs. As a counterpart, the appendix by Sebastian Casalaina-Martin shows that the degree of the algebraic Abel–Prym map is $2^{g-1}$ as well. |
| ArticleNumber | e11 |
| Author | Zakharov, Dmitry Len, Yoav |
| Author_xml | – sequence: 1 givenname: Yoav orcidid: 0000-0002-4997-6659 surname: Len fullname: Len, Yoav email: yoav.len@st-andrews.ac.uk organization: 1Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, UK; E-mail: yoav.len@st-andrews.ac.uk – sequence: 2 givenname: Dmitry surname: Zakharov fullname: Zakharov, Dmitry email: dvzakharov@gmail.com organization: 2Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, USA; E-mail: dvzakharov@gmail.com |
| BookMark | eNp1kM9Kw0AQhxepYK09-QIBL4Kk7p9spjlKsSoW9KDnZZPM2i1Ntu5uhd58DV_PJzGlBUX0NHP4fjM_vmPSa12LhJwyOmKUwaVpwohTzkYgD0ifU0lTSYus92M_IsMQFpRSxjhIgD45v7e-ms-dMZ_vHyGJc3Qem8Q4nzz6TZO8aW8xWgwn5NDoZcDhfg7I8_T6aXKbzh5u7iZXs7QSIo9pmYMQEjivtTRaFDXNYFwxgTXPxhlnRZYJ4BWUBWLXQQiDCCUzpmCgjcjFgJzt7q68e11jiGrh1r7tXiqe83EhuOSyoy52VOVdCB6NWnnbaL9RjKqtDdXZUFsbCrY0-0VXNupoXRu9tst_Muk-o5vS2_oFv4v8xX8BdIlyYg |
| CitedBy_id | crossref_primary_10_1016_j_disc_2025_114631 crossref_primary_10_1007_s00026_024_00707_0 crossref_primary_10_1017_S0305004123000518 crossref_primary_10_5802_alco_410 |
| Cites_doi | 10.1142/S0129167X92000357 10.1090/S0002-9947-01-02746-5 10.1007/s11856-018-1698-9 10.4310/ARKIV.2020.v58.n1.a5 10.1007/BF01418373 10.1142/9789814503365_0009 10.1016/j.jpaa.2016.12.029 10.1007/978-3-319-06514-4_7 10.1017/fms.2014.25 10.1016/j.disc.2013.11.008 10.1007/BF02392458 10.1006/jctb.1998.1861 10.2140/pjm.2001.201.479 10.1007/s10801-010-0247-3 10.4310/ACTA.2017.v218.n1.a2 10.2307/1970801 10.1007/s00574-014-0076-4 10.1090/S0002-9939-1984-0759646-4 10.1016/j.laa.2021.07.009 10.1007/BF01472135 10.1007/s00029-017-0379-6 10.1016/j.aim.2007.04.012 10.1006/aima.2000.1917 10.1007/BF02698887 10.4171/JEMS/678 10.1090/conm/465/09104 10.1016/j.jcta.2012.07.011 10.1093/imrn/rnu168 10.1090/S0894-0347-1994-1254134-8 10.1006/aima.1996.0050 10.1090/conm/564/11147 10.1017/fms.2019.40 10.1016/0166-218X(82)90033-6 10.1007/s00208-018-1646-3 10.1017/S0004972700025053 10.1007/BF01390330 |
| ContentType | Journal Article |
| Copyright | The Author(s), 2022. Published by Cambridge University Press The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the associated terms available at: https://uk.sagepub.com/en-gb/eur/reusing-open-access-and-sage-choice-content |
| Copyright_xml | – notice: The Author(s), 2022. Published by Cambridge University Press – notice: The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the associated terms available at: https://uk.sagepub.com/en-gb/eur/reusing-open-access-and-sage-choice-content |
| DBID | IKXGN AAYXX CITATION 8FE 8FG ABJCF AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1017/fms.2021.75 |
| DatabaseName | Cambridge University Press Wholly Gold Open Access Journals CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea SciTech Premium Collection (via ProQuest) ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (New) Engineering Collection ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Engineering Database |
| Database_xml | – sequence: 1 dbid: IKXGN name: Cambridge Univ. Press Open Journals (Free internet resource, activated by CARLI) url: http://journals.cambridge.org/action/login sourceTypes: Publisher – sequence: 2 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2050-5094 |
| ExternalDocumentID | 10_1017_fms_2021_75 |
| GroupedDBID | 09C 09E 0E1 0R~ 5VS 8FE 8FG AABES AABWE AACJH AAEED AAGFV AAKTX AANRG AARAB AASVR ABBXD ABDBF ABGDZ ABJCF ABKKG ABMWE ABQTM ABROB ACBMC ACGFS ACIMK ACIWK ACREK ACUIJ ACUYZ ACWGA ACZBM ACZUX ACZWT ADBBV ADCGK ADDNB ADFEC ADKIL ADOVH ADVJH AEBAK AEGXH AEHGV AENGE AEYYC AFFUJ AFKQG AFKRA AFLOS AFLVW AFUTZ AGABE AGBYD AGJUD AHQXX AHRGI AIGNW AIHIV AIOIP AISIE AJCYY AJPFC AJQAS ALMA_UNASSIGNED_HOLDINGS ALVPG ALWZO AQJOH ARABE AUXHV BBLKV BCNDV BENPR BGHMG BGLVJ BLZWO BMAJL C0O CBIIA CCPQU CCQAD CFAFE CHEAL CJCSC DOHLZ EBS EJD GROUPED_DOAJ HCIFZ HG- HZ~ I.6 IKXGN IOEEP IPYYG IS6 I~P JHPGK JQKCU KCGVB KFECR KQ8 L6V LW7 M-V M48 M7S M~E NIKVX O9- OK1 PTHSS PYCCK RAMDC RCA ROL RR0 S6- S6U SAAAG T9M UT1 WFFJZ WXY ZYDXJ AAYXX ABVKB ABXHF ACAJB ACDLN ACUHS AFFHD AFZFC AKMAY AMVHM CITATION PHGZM PHGZT PQGLB DWQXO PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c336t-b67335722da5fa39d0478c13ed248421944372c7b9ee12733fee7b1ff917af363 |
| IEDL.DBID | M7S |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000755592700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2050-5094 |
| IngestDate | Fri Jul 25 11:56:35 EDT 2025 Tue Nov 18 22:22:01 EST 2025 Sat Nov 29 02:40:39 EST 2025 Wed Mar 13 06:06:09 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 14T05 14H40 |
| Language | English |
| License | This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c336t-b67335722da5fa39d0478c13ed248421944372c7b9ee12733fee7b1ff917af363 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-4997-6659 |
| OpenAccessLink | https://www.cambridge.org/core/product/identifier/S205050942100075X/type/journal_article |
| PQID | 2628932525 |
| PQPubID | 2035935 |
| PageCount | 54 |
| ParticipantIDs | proquest_journals_2628932525 crossref_primary_10_1017_fms_2021_75 crossref_citationtrail_10_1017_fms_2021_75 cambridge_journals_10_1017_fms_2021_75 |
| PublicationCentury | 2000 |
| PublicationDate | 20220101 |
| PublicationDateYYYYMMDD | 2022-01-01 |
| PublicationDate_xml | – month: 01 year: 2022 text: 20220101 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Cambridge, UK |
| PublicationPlace_xml | – name: Cambridge, UK – name: Cambridge |
| PublicationTitle | Forum of Mathematics, Sigma |
| PublicationTitleAlternate | Forum of Mathematics, Sigma |
| PublicationYear | 2022 |
| Publisher | Cambridge University Press |
| Publisher_xml | – name: Cambridge University Press |
| References | 2017; 218 2019; 7 2001; 201 2014; 318 1981; 146 2012 2018; 226 2002; 553 1986; 273 2011; 33 1977; 41 1996; 121 2000; 154 2013; 120 2014; 45 2018; 24 1982; 45 2001; 353 2018; 372 1991; 422 1976; 14 2007; 215 1984; 92 2014; 2 1986; 85 2020 1982; 4 1994; 79 2017; 19 1972; 95 1998; 74 2017; 221 2018; II 1992; 1 1992; 3 1994; 7 S205050942100075X_r35 Arbarello (S205050942100075X_r4) 1985; 267 S205050942100075X_r38 S205050942100075X_r39 Lim (S205050942100075X_r36) 2012 Deninger (S205050942100075X_r24) 1991; 422 Creech (S205050942100075X_r23) 2020 S205050942100075X_r41 S205050942100075X_r42 S205050942100075X_r43 S205050942100075X_r44 S205050942100075X_r45 S205050942100075X_r46 S205050942100075X_r47 S205050942100075X_r48 S205050942100075X_r49 Masiewicki (S205050942100075X_r37) 1976; 222 Birkenhake (S205050942100075X_r13) 2004; 302 Mumford (S205050942100075X_r40) 1974 S205050942100075X_r50 S205050942100075X_r53 S205050942100075X_r10 S205050942100075X_r54 S205050942100075X_r55 S205050942100075X_r12 S205050942100075X_r56 S205050942100075X_r14 S205050942100075X_r15 S205050942100075X_r17 S205050942100075X_r19 Beauville (S205050942100075X_r11) 1982; 45 Eisenbud (S205050942100075X_r26) 1992; 1 S205050942100075X_r3 S205050942100075X_r5 S205050942100075X_r1 S205050942100075X_r6 S205050942100075X_r20 S205050942100075X_r7 Caporaso (S205050942100075X_r16) 2018; II S205050942100075X_r21 S205050942100075X_r8 S205050942100075X_r22 S205050942100075X_r9 S205050942100075X_r25 S205050942100075X_r27 S205050942100075X_r28 S205050942100075X_r29 Terras (S205050942100075X_r51) 2010; 51 Vologodsky (S205050942100075X_r52) 2002; 553 Alexeev (S205050942100075X_r2) 2002; 553 S205050942100075X_r30 Christ (S205050942100075X_r18) 2018 S205050942100075X_r31 S205050942100075X_r32 S205050942100075X_r33 S205050942100075X_r34 |
| References_xml | – volume: 372 start-page: 891 issue: 3–4 year: 2018 end-page: 914 article-title: Non-Archimedean and tropical theta functions publication-title: Math. Ann – year: 2020 article-title: Prym–Brill–Noether loci of special curves publication-title: Int. Math. Res. Not. IMRN – volume: 7 start-page: 589 issue: 3 year: 1994 end-page: 660 article-title: A compactification of the universal Picard variety over the moduli space of stable curves publication-title: J. Amer. Math. Soc – volume: 422 start-page: 201 year: 1991 end-page: 219 article-title: Motivic decomposition of abelian schemes and the Fourier transform publication-title: J. Reine Angew. Math – volume: 45 start-page: 357 issue: 3 year: 1982 end-page: 383 article-title: Sous-variétés spéciales des variétés de Prym publication-title: Compos. Math – volume: 24 start-page: 1391 issue: 2 year: 2018 end-page: 1410 article-title: Tropicalization of theta characteristics, double covers, and Prym varieties publication-title: Selecta Math. (N.S.) – volume: 3 start-page: 717 issue: 06 year: 1992 end-page: 797 article-title: The Ihara-Selberg zeta function of a tree lattice publication-title: Int. J. Math – volume: 1 start-page: 15 issue: 1 year: 1992 end-page: 30 article-title: Finite projective schemes in linearly general position publication-title: J. Algebraic Geom – volume: 79 start-page: 47 year: 1994 end-page: 129 article-title: Moduli of representations of the fundamental group of a smooth projective variety, I publication-title: Inst. Hautes Études Sci. Publ. Math – volume: 318 start-page: 10 year: 2014 end-page: 40 article-title: Critical groups of covering, voltage and signed graphs publication-title: Discrete Math – volume: 2 year: 2014 article-title: Canonical representatives for divisor classes on tropical curves and the matrix–tree theorem publication-title: Forum Math. Sigma – volume: II start-page: 635 year: 2018 end-page: 652 article-title: Recursive combinatorial aspects of compactified moduli spaces publication-title: Proceedings of the International Congress of Mathematicians (ICM 2018) – volume: 45 start-page: 807 issue: 4 year: 2014 end-page: 818 article-title: A simple characteristic-free proof of the Brill–Noether theorem publication-title: Bull. Braz. Math. Soc. (N.S.) – volume: 7 year: 2019 article-title: Geometric bijections for regular matroids, zonotopes and Ehrhart theory publication-title: Forum Math. Sigma – volume: 92 start-page: 329 issue: 3 year: 1984 end-page: 331 article-title: A new proof of the Ran-Matsusaka criterion for Jacobians publication-title: Proc. Amer. Math. Soc – volume: 74 start-page: 408 issue: 2 year: 1998 end-page: 410 article-title: A note on the zeta function of a graph publication-title: J. Combin. Theory Ser. B – volume: 553 start-page: 117 year: 2002 end-page: 124 article-title: Locus of indeterminacy of the Prym map publication-title: J. Reine Angew. Math – volume: 33 start-page: 349 issue: 3 year: 2011 end-page: 381 article-title: Metric properties of the tropical Abel-Jacobi map publication-title: J. Algebraic Combin – volume: 553 start-page: 73 year: 2002 end-page: 116 article-title: Degenerations of Prym varieties publication-title: J. Reine Angew. Math – volume: 4 start-page: 47 issue: 1 year: 1982 end-page: 74 article-title: Signed graphs publication-title: Discrete Appl. Math – volume: 85 start-page: 615 year: 1986 end-page: 635 article-title: Degenerations of Prym varieties and intersections of three quadrics publication-title: Invent. Math – volume: 221 start-page: 2420 issue: 10 year: 2017 end-page: 2430 article-title: Brill–Noether theory for cyclic covers publication-title: J. Pure Appl. Algebra – volume: 154 start-page: 132 issue: 1 year: 2000 end-page: 195 article-title: Zeta functions of finite graphs and coverings, part II publication-title: Adv. Math – volume: 95 start-page: 281 issue: 2 year: 1972 end-page: 356 article-title: The intermediate Jacobian of the cubic threefold publication-title: Ann. Math – start-page: 5408 issue: 23 year: 2012 end-page: 5504 article-title: A note on Brill-Noether theory and rank determining sets for metric graphs publication-title: Int. Math. Res. Not. IMRN – volume: 120 start-page: 164 issue: 1 year: 2013 end-page: 182 article-title: Chip-firing games, potential theory on graphs, and spanning trees publication-title: J. Combin. Theory Ser. A – volume: 353 start-page: 3045 issue: 8 year: 2001 end-page: 3095 article-title: Compactifying the relative Jacobian over families of reduced curves publication-title: Trans. Amer. Math. Soc – volume: 226 start-page: 351 year: 2018 end-page: 385 article-title: Enumerative geometry of elliptic curves on toric surfaces publication-title: Isr. J. Math – volume: 218 start-page: 55 issue: 1 year: 2017 end-page: 135 article-title: A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold publication-title: Acta Math – volume: 41 start-page: 149 issue: 2 year: 1977 end-page: 196 article-title: Prym varieties and the Schottky problem publication-title: Invent. Math – volume: 14 start-page: 233 issue: 2 year: 1976 end-page: 248 article-title: Double covers of graphs publication-title: Bull. Aust. Math. Soc – volume: 146 start-page: 25 issue: 1–2 year: 1981 end-page: 102 article-title: The structure of the Prym map publication-title: Acta Math – volume: 19 start-page: 659 year: 2017 end-page: 723 article-title: Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties publication-title: J. Eur. Math. Soc – volume: 215 start-page: 766 issue: 2 year: 2007 end-page: 788 article-title: Riemann–Roch and Abel–Jacobi theory on a finite graph publication-title: Adv. Math – volume: 273 start-page: 647 issue: 4 year: 1986 end-page: 651 article-title: Sur l’anneau de Chow d’une variété abélienne publication-title: Math. Ann – volume: 121 start-page: 124 issue: 1 year: 1996 end-page: 165 article-title: Zeta functions of finite graphs and coverings publication-title: Adv. Math – volume: 201 start-page: 479 issue: 2 year: 2001 end-page: 509 article-title: A Riemann singularities theorem for Prym theta divisors, with applications publication-title: Pacific J. Math – ident: S205050942100075X_r9 doi: 10.1142/S0129167X92000357 – ident: S205050942100075X_r27 doi: 10.1090/S0002-9947-01-02746-5 – ident: S205050942100075X_r33 doi: 10.1007/s11856-018-1698-9 – ident: S205050942100075X_r20 doi: 10.4310/ARKIV.2020.v58.n1.a5 – ident: S205050942100075X_r10 doi: 10.1007/BF01418373 – ident: S205050942100075X_r47 doi: 10.1142/9789814503365_0009 – ident: S205050942100075X_r14 – ident: S205050942100075X_r45 doi: 10.1016/j.jpaa.2016.12.029 – ident: S205050942100075X_r39 doi: 10.1007/978-3-319-06514-4_7 – ident: S205050942100075X_r54 doi: 10.1017/fms.2014.25 – ident: S205050942100075X_r43 doi: 10.1016/j.disc.2013.11.008 – ident: S205050942100075X_r25 doi: 10.1007/BF02392458 – ident: S205050942100075X_r41 doi: 10.1006/jctb.1998.1861 – ident: S205050942100075X_r48 doi: 10.2140/pjm.2001.201.479 – ident: S205050942100075X_r5 doi: 10.1007/s10801-010-0247-3 – ident: S205050942100075X_r32 doi: 10.4310/ACTA.2017.v218.n1.a2 – ident: S205050942100075X_r21 doi: 10.2307/1970801 – ident: S205050942100075X_r42 doi: 10.1007/s00574-014-0076-4 – volume: 267 volume-title: Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] year: 1985 ident: S205050942100075X_r4 – ident: S205050942100075X_r30 – ident: S205050942100075X_r22 doi: 10.1090/S0002-9939-1984-0759646-4 – ident: S205050942100075X_r1 – volume: 45 start-page: 357 year: 1982 ident: S205050942100075X_r11 article-title: Sous-variétés spéciales des variétés de Prym publication-title: Compos. Math – volume: 1 start-page: 15 year: 1992 ident: S205050942100075X_r26 article-title: Finite projective schemes in linearly general position publication-title: J. Algebraic Geom – ident: S205050942100075X_r55 doi: 10.1016/j.laa.2021.07.009 – ident: S205050942100075X_r34 – volume-title: Orientations, Break Divisors and Compactified Jacobians year: 2018 ident: S205050942100075X_r18 – ident: S205050942100075X_r12 doi: 10.1007/BF01472135 – ident: S205050942100075X_r31 doi: 10.1007/s00029-017-0379-6 – ident: S205050942100075X_r6 doi: 10.1016/j.aim.2007.04.012 – volume: II start-page: 635 year: 2018 ident: S205050942100075X_r16 article-title: Recursive combinatorial aspects of compactified moduli spaces publication-title: Proceedings of the International Congress of Mathematicians (ICM 2018) – start-page: 325 volume-title: Contributions to Analysis (A Collection of Papers Dedicated to Lipman Bers) year: 1974 ident: S205050942100075X_r40 – volume: 553 start-page: 73 year: 2002 ident: S205050942100075X_r2 article-title: Degenerations of Prym varieties publication-title: J. Reine Angew. Math – volume: 553 start-page: 117 year: 2002 ident: S205050942100075X_r52 article-title: Locus of indeterminacy of the Prym map publication-title: J. Reine Angew. Math – volume: 422 start-page: 201 year: 1991 ident: S205050942100075X_r24 article-title: Motivic decomposition of abelian schemes and the Fourier transform publication-title: J. Reine Angew. Math – ident: S205050942100075X_r50 doi: 10.1006/aima.2000.1917 – volume: 51 start-page: 177 year: 2010 ident: S205050942100075X_r51 – ident: S205050942100075X_r46 doi: 10.1007/BF02698887 – ident: S205050942100075X_r35 – volume: 302 volume-title: Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] year: 2004 ident: S205050942100075X_r13 – start-page: 5408 year: 2012 ident: S205050942100075X_r36 article-title: A note on Brill-Noether theory and rank determining sets for metric graphs publication-title: Int. Math. Res. Not. IMRN – ident: S205050942100075X_r17 doi: 10.4171/JEMS/678 – ident: S205050942100075X_r38 doi: 10.1090/conm/465/09104 – ident: S205050942100075X_r8 doi: 10.1016/j.jcta.2012.07.011 – ident: S205050942100075X_r7 doi: 10.1093/imrn/rnu168 – ident: S205050942100075X_r15 doi: 10.1090/S0894-0347-1994-1254134-8 – ident: S205050942100075X_r49 doi: 10.1006/aima.1996.0050 – ident: S205050942100075X_r3 doi: 10.1090/conm/564/11147 – ident: S205050942100075X_r44 doi: 10.1017/fms.2019.40 – year: 2020 ident: S205050942100075X_r23 article-title: Prym–Brill–Noether loci of special curves publication-title: Int. Math. Res. Not. IMRN – ident: S205050942100075X_r56 doi: 10.1016/0166-218X(82)90033-6 – ident: S205050942100075X_r28 doi: 10.1007/s00208-018-1646-3 – ident: S205050942100075X_r53 doi: 10.1017/S0004972700025053 – volume: 222 start-page: 221 volume-title: ‘Universal properties of Prym varieties with an application to algebraic curves of genus five’, year: 1976 ident: S205050942100075X_r37 – ident: S205050942100075X_r29 doi: 10.1007/BF01390330 – ident: S205050942100075X_r19 |
| SSID | ssj0001127577 |
| Score | 2.2650802 |
| Snippet | We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret... |
| SourceID | proquest crossref cambridge |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| SubjectTerms | Algebra Algebraic and Complex Geometry Decomposition Graphs Theorems Trees |
| SummonAdditionalLinks | – databaseName: Cambridge University Press Wholly Gold Open Access Journals dbid: IKXGN link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LS8NAEB5q60EPvsVqlRyKiBDD7jbZ7FHEqhRLQYXcQrIPLNgHSS1482_49_wl7ibbFKEHL17DQCYzu5lvdme-AWhzQX2chtKloZRuR4Xc1bgZuZwEGkAnOocWSTFsgvb7YRSxQQ2iRS-MKausOA6Km_xiPtq0pD_1hqKsoZGZ94TNEDadnWBUBL7IM4eWnnVBbA2_Bg2NYDCuQ-OhF931l-cvhtmcUtuyZ1ik1cjQd2N0ZWoOl0QLvwPW7_91EYS62_-n_g5sWWDqXJdPdqEmx3uw-Vixuub7cNEb6l3xOlHq-_Mrd8oeyJGjYa8zyD5Gztzk3Yag9QBeurfPN_eunbSgfUKCmZsGlBCfYiwSXyWECcPZwxGRAndCrSHrmOs9TlMmpbYbIUpKmiKldLKXKBKQQ6iPJ2N5BE6aJgwJJRRSGhzo9eGzgHHEGOcpCThtwnlloNh-bR6XtWZU76w8Nj6Iqd-Ey4XdY275ys3YjLfVwu1KeFrSdKwWay0cuHw3DnTSSbCP_eO_6nYCG9i0QRRHMS2oz7J3eQrrfD4b5tmZXWo_xvbnlA priority: 102 providerName: Cambridge University Press |
| Title | Kirchhoff’s theorem for Prym varieties |
| URI | https://www.cambridge.org/core/product/identifier/S205050942100075X/type/journal_article https://www.proquest.com/docview/2628932525 |
| Volume | 10 |
| WOSCitedRecordID | wos000755592700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAEN databaseName: Cambridge Univ. Press Open Journals (Free internet resource, activated by CARLI) customDbUrl: eissn: 2050-5094 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001127577 issn: 2050-5094 databaseCode: IKXGN dateStart: 20130101 isFulltext: true titleUrlDefault: http://journals.cambridge.org/action/login providerName: Cambridge University Press – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2050-5094 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001127577 issn: 2050-5094 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2050-5094 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001127577 issn: 2050-5094 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 2050-5094 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001127577 issn: 2050-5094 databaseCode: M7S dateStart: 20140101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2050-5094 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001127577 issn: 2050-5094 databaseCode: BENPR dateStart: 20140101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEF609aAH32K1lhyKiBAlu0k2exKVVqUYig_oLST7wIJ92NSCF_Fv-Pf8Je4k24ZC8eIlEDKQMDOZ1858g1CdC-rhJJA2DaS0XRVwW8fNjs2JrwPoWOfQIs6WTdAwDDod1jYFt9S0VU5tYmaoxYBDjfwc-zo1INjD3sXwzYatUXC6alZoLKMyoCTgrHXvsaixAHo5pWYsD5CiVQ8gurFzBn2FBZjCvFOat8mZo2lu_PcTN9G6CTGty1wnttCS7G-jtfsZPmu6g05aXa3fLwOlfr6-UyufZuxZOoC12qOPnjWBDBqgVnfRc7PxdH1rm50JmrvEH9uJTwnxKMYi9lRMmAD0He4QKbAbuNo8uXBQx2nCpNTcIURJSRNHKZ22xYr4ZA-V-oO-3EdWksTMEUooR2k3ryXtMZ9xhzHOE-JzWkHHMwZGRvPTKO8ao_ofSSPgdES9CjqdcjfiBnkcFmC8Liauz4iHOeDGYrLqVAbFuwsBHPz9-BCtYhhjyEopVVQaj97lEVrhk3E3HdVQ-aoRth9qWX6u7-5anZuwlqkWXD8bvwrU1q8 |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LS8NAEB5qFdSDb7FaNYcqIkTJbpLNHkRELS19ULBCbzHZ7GLBPmxqpTf_hn_CH-UvcTePFqF468FzhuyyMzuvnfkGoMACYiHf4TpxONdN4TBd-s2GzrAtHWhPxtCBFw2bIPW602rRRga-0l4YVVaZ6sRIUQc9pnLkl8iWoQFGFrKu-6-6mhqlXlfTERqxWFT4-F2GbOFV-U7y9wSh4n3ztqQnUwXk-tge6r5NMLYIQoFnCQ_TQOHTMAPzAJmOKS-wqZ6yGPEp54Y07lhwTnxDCBnYeALbWP53ARZNpf2jUsGHaU5HoaUTkrQBKmRq0VGQ4Mi4UHWMU_CG30bwtw2IDFtx_b8dyQasJS60dhPL_CZkeHcLVmsT_NlwG84qbbmr554Q3x-foRZ3a3Y06aBrjcG4o41UhkBBye7A41y2ugvZbq_L90DzfY8agQiEIaQbIyXZojZlBqWM-dhmJAenE4a5yc0O3bgqjkgdELqKsy6xcnCectNlCbK6GvDxMpu4MCHux4Ais8nyKc-na08Zvv_352NYLjVrVbdarlcOYAWplo0obZSH7HDwxg9hiY2G7XBwFAmwBk_zFo8fkhQsaA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Kirchhoff%E2%80%99s+theorem+for+Prym+varieties&rft.jtitle=Forum+of+mathematics.+Sigma&rft.au=Len%2C+Yoav&rft.au=Zakharov%2C+Dmitry&rft.date=2022-01-01&rft.pub=Cambridge+University+Press&rft.eissn=2050-5094&rft.volume=10&rft_id=info:doi/10.1017%2Ffms.2021.75 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2050-5094&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2050-5094&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2050-5094&client=summon |