Group actions on local moduli space of holomorphic vector bundles
We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space.
Saved in:
| Published in: | Canadian mathematical bulletin Vol. 66; no. 2; pp. 553 - 567 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Canada
Canadian Mathematical Society
01.06.2023
Cambridge University Press |
| Subjects: | |
| ISSN: | 0008-4395, 1496-4287 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space. |
|---|---|
| AbstractList | We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space. |
| Author | Doan, An-Khuong |
| Author_xml | – sequence: 1 givenname: An-Khuong orcidid: 0000-0002-0565-6549 surname: Doan fullname: Doan, An-Khuong email: an-khuong.doan@imj-prg.fr organization: IMJ-PRG, UMR 7586, Sorbonne Université, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France |
| BookMark | eNp9kEtLAzEQx4NUsK1-AG8Bz6t57SPHUrQVCh7U85LNw6ZkN2uyK_jtzdKCoOgcZgb-85vXAsw632kArjG6ZTind88IoYpRnhOSsuTPwBwzXmSMVOUMzCc5m_QLsIjxgBAu8zKfg9Um-LGHQg7WdxH6DjovhYOtV6OzMPZCaugN3HvnWx_6vZXwQ8vBB9iMnXI6XoJzI1zUV6e4BK8P9y_rbbZ72jyuV7tMUlwOmZCcVEoSUhiGFGoKrIgxKhdUcsGM4gWhgudSGyk0lajSqlG4InmDkU5Gl-Dm2LcP_n3UcagPfgxdGlmTCnGWzuEsVZXHKhl8jEGbWtpBTMcNQVhXY1RP_6p__SuR-AfZB9uK8PkvQ0-MaJtg1Zv-Xupv6gtW834z |
| CitedBy_id | crossref_primary_10_1007_s13348_024_00450_y |
| Cites_doi | 10.1007/s12220-020-00411-4 10.1007/BF01404124 10.1007/s00229-002-0337-1 10.1007/s13373-015-0070-1 10.1016/S0022-4049(00)00121-3 10.1016/j.aim.2009.12.009 10.1090/S0002-9947-1968-0217093-3 10.1007/s00229-021-01289-4 10.1016/j.geomphys.2021.104237 10.1007/b138372 10.2977/prims/1195173613 |
| ContentType | Journal Article |
| Copyright | The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society |
| Copyright_xml | – notice: The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society |
| DBID | AAYXX CITATION 3V. 7XB 8FE 8FG 8FK 8FQ 8FV ABJCF ABUWG AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS Q9U |
| DOI | 10.4153/S0008439522000522 |
| DatabaseName | CrossRef ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Canadian Business & Current Affairs Database Canadian Business & Current Affairs Database (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea SciTech Premium Collection 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) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Basic ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central CBCA Complete (Alumni Edition) ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection CBCA Complete ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) Engineering Collection |
| DatabaseTitleList | Engineering Database CrossRef |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1496-4287 |
| EndPage | 567 |
| ExternalDocumentID | 10_4153_S0008439522000522 |
| GroupedDBID | --Z -~X 09C 09E 5.9 69Q 6J9 8FQ AABWE AAEED AAGFV AANRG AASVR AAUKB AAYEQ AAYJJ ABBZL ABCQX ABGDZ ABJCF ABMYL ABUWG ABXAU ABZCX ABZEH ACGFO ACIPV ACKIV ACNCT ACQFJ ACYZP ACZWT ADDNB ADGEJ ADKIL ADOCW ADOVH ADVJH AEBAK AEBPU AENCP AETEA AFKQG AFKRA AFLVW AGABE AGBYD AGJUD AGOOT AHRGI AI. AIDBO AIOIP AJCYY AJPFC ALMA_UNASSIGNED_HOLDINGS AQJOH ARZZG ATUCA AYIQA BBLKV BCGOX BENPR BESQT BGLVJ BLZWO CCPQU CCQAD CCUQV CFBFF CGQII CHEAL CJCSC DOHLZ DWQXO EBS EGQIC EJD FRP HCIFZ HF~ IH6 IOO JHPGK KCGVB KFECR L7B LW7 M7S MVM NZEOI OHT OK1 P2P PTHSS RCA RCD ROL S10 TR2 UPT VH1 WFFJZ WH7 XJT ZCG ZMEZD 0R~ AAXMD AAYXX ABUFD ABVKB ABVZP ABXHF ACDLN ADIYS AFFHD AFZFC AKMAY AMVHM CITATION PHGZM PHGZT PQGLB 3V. 7XB 8FE 8FG 8FK L6V PKEHL PQEST PQQKQ PQUKI Q9U |
| ID | FETCH-LOGICAL-c317t-ac928dc226f40d0b61d2ffd5a3c9a4fd9623a95cefcae3c08edbd1825b10eeee3 |
| IEDL.DBID | BENPR |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000852890200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0008-4395 |
| IngestDate | Fri Jul 25 12:01:38 EDT 2025 Sat Nov 29 05:31:07 EST 2025 Tue Nov 18 22:05:04 EST 2025 Wed Mar 13 05:49:58 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | 14B10 Deformation theory moduli theory equivariance structure semi-universality 32G05 14D15 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c317t-ac928dc226f40d0b61d2ffd5a3c9a4fd9623a95cefcae3c08edbd1825b10eeee3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-0565-6549 |
| PQID | 2809457594 |
| PQPubID | 4573633 |
| PageCount | 15 |
| ParticipantIDs | proquest_journals_2809457594 crossref_citationtrail_10_4153_S0008439522000522 crossref_primary_10_4153_S0008439522000522 cambridge_journals_10_4153_S0008439522000522 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-06-01 |
| PublicationDateYYYYMMDD | 2023-06-01 |
| PublicationDate_xml | – month: 06 year: 2023 text: 2023-06-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Canada |
| PublicationPlace_xml | – name: Canada – name: Montreal |
| PublicationTitle | Canadian mathematical bulletin |
| PublicationTitleAlternate | Can. Math. Bull |
| PublicationYear | 2023 |
| Publisher | Canadian Mathematical Society Cambridge University Press |
| Publisher_xml | – name: Canadian Mathematical Society – name: Cambridge University Press |
| References | 2022; 167 2001; 162 2015; 5 2021; 31 1968; 130 1989; 25 2010; 224 2003; 110 1972; 15 1980; 257 S0008439522000522_r1 Rim (S0008439522000522_r18) 1980; 257 S0008439522000522_r3 S0008439522000522_r4 S0008439522000522_r5 S0008439522000522_r6 S0008439522000522_r14 S0008439522000522_r7 S0008439522000522_r15 S0008439522000522_r9 S0008439522000522_r16 S0008439522000522_r17 S0008439522000522_r19 Catanese (S0008439522000522_r2) 2013 Kuranishi (S0008439522000522_r13) 1971 S0008439522000522_r20 S0008439522000522_r10 S0008439522000522_r11 S0008439522000522_r12 Douady (S0008439522000522_r8) 1964 |
| References_xml | – volume: 25 start-page: 301 year: 1989 end-page: 320 article-title: Kuranishi family of vector bundles and algebraic description of the moduli space of Einstein–Hermitian connections publication-title: Publ. Res. Inst. Math. Sci. – volume: 224 start-page: 772 issue: 3 year: 2010 end-page: 826 article-title: Unifying derived deformation theories publication-title: Adv. Math. – volume: 5 start-page: 287 year: 2015 end-page: 449 article-title: Topological methods in moduli theory publication-title: Bull. Math. Sci. – volume: 31 start-page: 3698 year: 2021 end-page: 3712 article-title: A counter-example to the equivariance structure on semi-universal deformation publication-title: J. Geom. Anal. – volume: 15 start-page: 171 year: 1972 end-page: 198 article-title: Über die deformation isolierter Singularitäten analytischer Mengen publication-title: Invent. Math. – volume: 130 start-page: 208 issue: 2 year: 1968 end-page: 222 article-title: Functors of Artin rings publication-title: Trans. Amer. Math. Soc. – volume: 167 start-page: 793 year: 2022 end-page: 808 article-title: Equivariant Kuranishi family of complex compact manifolds publication-title: Manuscripta Math. – volume: 257 start-page: 217 issue: 1 year: 1980 end-page: 226 article-title: Equivariant $G$ -structure on versal deformations publication-title: Trans. Amer. Math. Soc. – volume: 162 start-page: 209 issue: 2–3 year: 2001 end-page: 250 article-title: DG coalgebras as formal stacks publication-title: J. Pure Appl. Algebra – volume: 110 start-page: 237 year: 2003 end-page: 249 article-title: Local moduli spaces and Kuranishi maps publication-title: Manuscripta Math. – start-page: 161 volume-title: Handbook of moduli year: 2013 ident: S0008439522000522_r2 – ident: S0008439522000522_r4 doi: 10.1007/s12220-020-00411-4 – ident: S0008439522000522_r9 doi: 10.1007/BF01404124 – ident: S0008439522000522_r15 – ident: S0008439522000522_r12 doi: 10.1007/s00229-002-0337-1 – ident: S0008439522000522_r3 doi: 10.1007/s13373-015-0070-1 – ident: S0008439522000522_r10 doi: 10.1016/S0022-4049(00)00121-3 – ident: S0008439522000522_r17 doi: 10.1016/j.aim.2009.12.009 – ident: S0008439522000522_r14 – ident: S0008439522000522_r19 doi: 10.1090/S0002-9947-1968-0217093-3 – ident: S0008439522000522_r5 – ident: S0008439522000522_r7 doi: 10.1007/s00229-021-01289-4 – ident: S0008439522000522_r6 – volume-title: Deformations of compact complex manifolds year: 1971 ident: S0008439522000522_r13 – ident: S0008439522000522_r1 doi: 10.1016/j.geomphys.2021.104237 – ident: S0008439522000522_r11 doi: 10.1007/b138372 – volume: 257 start-page: 217 year: 1980 ident: S0008439522000522_r18 article-title: Equivariant $G$ -structure on versal deformations publication-title: Trans. Amer. Math. Soc. – ident: S0008439522000522_r16 doi: 10.2977/prims/1195173613 – ident: S0008439522000522_r20 – start-page: 7 volume-title: Séminaire Bourbaki year: 1964 ident: S0008439522000522_r8 |
| SSID | ssj0017575 |
| Score | 2.2887928 |
| Snippet | We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli... |
| SourceID | proquest crossref cambridge |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 553 |
| SubjectTerms | Lie groups Mathematical analysis |
| Title | Group actions on local moduli space of holomorphic vector bundles |
| URI | https://www.cambridge.org/core/product/identifier/S0008439522000522/type/journal_article https://www.proquest.com/docview/2809457594 |
| Volume | 66 |
| WOSCitedRecordID | wos000852890200001&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: PRVPQU databaseName: Canadian Business & Current Affairs Database customDbUrl: eissn: 1496-4287 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: 8FQ dateStart: 20190301 isFulltext: true titleUrlDefault: https://search.proquest.com/cbcacomplete providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1496-4287 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: M7S dateStart: 20190301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1496-4287 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0017575 issn: 0008-4395 databaseCode: BENPR dateStart: 20190301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8JAEJ4oeNCDbyOKZA-ejBuXPrcngwbiRYKvhFvT7iMhgRYp8PudbUuRmHCxx3Y32exsZ7557HwAtwKVIuIGRmOE39SxNKPoZymqIt9Rvqe5ZFFONuH3-3w4DAZlwC0ryypXOjFX1DIVJkb-YHF0RAybpPM4_aaGNcpkV0sKjV2om05lTg3qT93-4L3KI_iuX3AYME7R9LpFXhONlm3uCDNu3llWnu-yfndX2LRSm0o6tzy9o_-u-RgOS8xJOsUhOYEdlZzCwWvVsDU7g04egyLFLYeMpAnJjRyZpHIxHhFUO0KRVBOjKycpymYkyDIP-JN4Yfo0ZOfw1et-Pr_Qkl2BCsQMcxqJwOJSIPzSDpMs9trS0lq6kS2CyNEyQGAUBa5QWkTKFowrGUv0Rty4zRQ-9gXUkjRRl0BQSUnbVx7OVE6scajHVMCUE0llMFwD7qudDct_JAvR_TCCCP8IogFstfmhKDuVG8KM8bYpd9WUadGmY9vg5kpc69WsZXW1_fM17BvK-aJcrAm1-WyhbmBPLOejbNaCXd57a5XHsGUqST9-ADek4RU |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LS8QwEB50FdSDb_FtDnoRgzFtt-1BRHygqIuggrfaJhNY0K1udxX_lL_RSbpdFWFvHuyxTUrbmc73TWYyA7CpyCgSbxA8I_rNfWkEJz8LOaahj2HdRFqkrtlE2GhE9_fx9RB8VHthbFplZROdoda5smvkuzIiR8R2k_QPnl-47Rplo6tVC41SLS7w_Y1ctmL__JjkuyXl6cnt0RnvdRXgirCyw1MVy0groh3GF1pk9T0tjdFB6qk49Y2OiRCkcaDQqBQ9JSLUmSYWHmR7Aunw6L7DMOJb6-9SBW_6UYswCMuOCSLiBPRBGUUliPTsjmQR2XNSuuia_F7L4Scm_oQEh3OnU__tC03DZI9Rs8PyF5iBIWzNwsRVvxxtMQeHboWNlXs4Cpa3mINw9pTr7mOTkVFVyHLDLBI85aR5TcVeXTiDZV1bhaKYh7s_eYcFqLXyFi4CIxOsvRDrNBP9zNDQusBYoJ9qtAx1CXb6kkx6FqBIyLmygk9-CX4JRCXsRPXqsNt2II-Dpmz3pzyXRUgGDV6t1OPrab50Y3nw5Q0YO7u9ukwuzxsXKzAuidKViXGrUOu0u7gGo-q10yza6071GTz8tSZ9Al6FP28 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3PT9swFH4qDKHtMGBjWjfYfBgXNAvj_D5MExqrVpVVSIDUW5bYz1IlSBhpO_Gv8dft2Ula0KTeeliOiR0l8Zf3fc_Pfg_gkyKjSLpB8JzkN_elEZz8LOSYRT5GoYm1yFyxiWg4jEej5LwDD-1eGLussrWJzlDrUtk58iMZkyNiq0n6R6ZZFnF-2vt6-5vbClI20tqW06ghMsD7P-S-VV_6pzTWB1L2vl9--8GbCgNcEW9OeKYSGWtFEsT4Qos8PNbSGB1knkoy3-iExEGWBAqNytBTIkada1LkQX4skA6P7rsGzyKfdIJbNngxj2BEQVRXTxAxJ9IP6ogq0aVndyeL2J6T0kXa5OO8Dk_58Sk9OM7rbf3PX2sbXjZKm53Uv8YOdLB4BS9-ztPUVq_hxM28sXpvR8XKgjlqZzelnl6PGRlbhaw0zDLETUmIHCs2c2EOlk9tdopqF65W8g5vYL0oC3wLjEyz9iIMqSf6uaGmocBEoJ9ptMq1C5_no5o2lqFKyemyIEj_AUEXRDvwqWrys9syIdfLuhzOu9zWyUmWNd5robJ4mgVO3i2__BE2CUDpWX84eA_PJSm9er3cHqxP7qa4DxtqNhlXdx_cX8Dg16qB9BeR-Eg1 |
| 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=Group+actions+on+local+moduli+space+of+holomorphic+vector+bundles&rft.jtitle=Canadian+mathematical+bulletin&rft.au=An-Khuong+Doan&rft.date=2023-06-01&rft.pub=Cambridge+University+Press&rft.issn=0008-4395&rft.volume=66&rft.issue=2&rft.spage=553&rft.epage=567&rft_id=info:doi/10.4153%2FS0008439522000522&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0008-4395&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0008-4395&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0008-4395&client=summon |