Complex hyperbolic orbifolds and hybrid lattices
A class of complex hyperbolic lattices in PU (2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [ 1 , 10 ] and [ 24 ]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in P 2 to constru...
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| Abstract | A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids. |
|---|---|
| AbstractList | A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids. A class of complex hyperbolic lattices in PU (2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [1, 10] and [24]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in $$\mathbb {P}^2$$ P 2 to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [18] and [19], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [25] shows that two of the Deligne-Mostow lattices in PU (2, 1) can be seen as hybrids of lattices in PU (1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids. A class of complex hyperbolic lattices in PU(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [1, 10] and [24]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in P2 to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [18] and [19], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [25] shows that two of the Deligne-Mostow lattices in PU(2, 1) can be seen as hybrids of lattices in PU(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids. |
| ArticleNumber | 28 |
| Author | Falbel, Elisha Pasquinelli, Irene |
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| Cites_doi | 10.1007/s10711-011-9609-9 10.2140/pjm.2019.302.201 10.1090/conm/501/09838 10.2140/gtm.1998.1.511 10.1007/978-1-4757-9286-7_7 10.2140/pjm.1980.86.171 10.1007/BF02698928 10.1007/BF01458537 10.1007/BF02831623 10.1007/s00222-015-0600-1 10.1016/B978-0-12-001011-0.50014-2 10.1090/S0273-0979-1987-15510-8 10.1090/ecgd/299 10.1007/s10240-005-0032-3 10.1093/oso/9780198537939.001.0001 10.2140/agt.2020.20.925 10.1307/mmj/1592532044 10.1016/j.topol.2019.106918 10.1007/BF02831622 10.23943/princeton/9780691144771.001.0001 10.1007/s10711-019-00506-5 10.2969/jmsj/02910091 10.1007/s11511-006-0001-9 10.1007/978-1-4757-6720-9 10.1007/978-3-322-92886-3 |
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| References | DerauxMParkerJRPaupertJNew nonarithmetic complex hyperbolic lattices IIMichigan Math. J.2021701135205425509110.1307/mmj/159253204407390741 PasquinelliIFundamental domains and presentations for the Deligne-Mostow lattices with 2-fold symmetryPacific J. Math.20193021201247402877210.2140/pjm.2019.302.2011436.22007 PasquinelliIDeligne-Mostow lattices with three fold symmetry and cone metrics on the sphereConform. Geom. Dyn.201620235281352298310.1090/ecgd/2991354.32014 Parker, John R.: Complex hyperbolic lattices. In Discrete groups and geometric structures, volume 501 of Contemp. Math., pages 1–42. Amer. Math. Soc., Providence, RI, (2009) ParkerJRCone metrics on the sphere and Livné’s latticesActa Math.20061961164223720510.1007/s11511-006-0001-91100.57017 Dashyan, R.: A construction of representations of 3-manifold groups into PU(2,1) through Lefschetz fibrations. arXiv:1909.10229 (2019) DerauxMA new nonarithmetic lattice in PU(3,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm PU}(3,1)$$\end{document}Algebr. Geom. Topol.2020202925963409231510.2140/agt.2020.20.9251457.22003 MostowGDBraids, hypergeometric functions, and latticesBull. Am. Math. Soc. (N.S.)198716222524687695910.1090/S0273-0979-1987-15510-80639.22005 Barthel, G., Hirzebruch, F., Höfer, T.: Geradenkonfigurationen und Algebraische Flächen. In: Aspects of Mathematics, D4. Friedr. Vieweg & Sohn, Braunschweig (1987) Paupert, Julien, Wells, Joseph: Hybrid lattices and thin subgroups of picard modular groups. arXiv preprint arXiv:1806.01438, (2019) TakeuchiKArithmetic triangle groupsJ. Math. Soc. Japan19772919110642974410.2969/jmsj/029100910344.20035 Thurston, William P.: Shapes of polyhedra and triangulations of the sphere. In The Epstein birthday schrift, volume 1 of Geom. Topol. Monogr., pages 511–549. Geom. Topol. Publ., Coventry, (1998) YamazakiTYoshidaMOn Hirzebruch’s examples of surfaces with c12=3c2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c^{2}_{1}=3c_{2}$$\end{document}Math. Ann.1984266442143173552510.1007/BF014585370513.14008 Hirzebruch, F.: Arrangements of lines and algebraic surfaces. In: Arithmetic and geometry, Vol. II, volume 36 of Progr. Math., pp. 113–140. Birkhäuser, Boston (1983) Goldman, W. M.: Complex hyperbolic geometry. In: Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (1999). Oxford Science Publications MostowGDGeneralized Picard lattices arising from half-integral conditionsInst. Hautes Études Sci. Publ. Math.1986639110684965210.1007/BF028316230615.22009 CouwenbergWHeckmanGLooijengaEGeometric structures on the complement of a projective arrangementPubl. Math. Inst. Hautes Études Sci.200510169161221704710.1007/s10240-005-0032-31083.14039 MostowGDOn a remarkable class of polyhedra in complex hyperbolic spacePac. J. Math.198086117127658687610.2140/pjm.1980.86.1710456.22012 WellsJNon-arithmetic hybrid lattices in PU(2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rm PU(2,1)$$\end{document}Geom. Dedicata.2020208111414291310.1007/s10711-019-00506-51441.22023 Kobayashi, R.: Uniformization of complex surfaces. In: Kähler metric and moduli spaces, volume 18 of Adv. Stud. Pure Math., pp. 313–394. Academic Press, Boston, MA (1990) GromovMPiatetski-ShapiroINonarithmetic groups in Lobachevsky spacesInst. Hautes Études Sci. Publ. Math.1988669310393213510.1007/BF026989280649.22007 DelignePMostowGDMonodromy of hypergeometric functions and nonlattice integral monodromyInst. Hautes Études Sci. Publ. Math.19866358984965110.1007/BF028316220615.22008 Tretkoff, Paula: Complex ball quotients and line arrangements in the projective plane, volume 51 of Mathematical Notes. Princeton University Press, Princeton, NJ, 2016. With an appendix by Hans-Christoph Im Hof DerauxMParkerJRPaupertJNew non-arithmetic complex hyperbolic latticesInvent. Math.20162033681771346136510.1007/s00222-015-0600-11337.22007 Maclachlan, Colin, Reid, Alan W.: The arithmetic of hyperbolic 3-manifolds. Graduate Texts in Mathematics, vol. 219. Springer-Verlag, New York (2003) PaupertJNon-discrete hybrids in SU(2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm SU}(2,1)$$\end{document}Geom. Dedicata.2012157259268289348810.1007/s10711-011-9609-91271.22008 762_CR15 762_CR11 762_CR10 T Yamazaki (762_CR26) 1984; 266 762_CR3 M Deraux (762_CR7) 2021; 70 762_CR8 I Pasquinelli (762_CR19) 2019; 302 GD Mostow (762_CR14) 1987; 16 I Pasquinelli (762_CR18) 2016; 20 P Deligne (762_CR5) 1986; 63 762_CR1 JR Parker (762_CR16) 2006; 196 762_CR24 762_CR23 M Deraux (762_CR6) 2016; 203 762_CR21 GD Mostow (762_CR13) 1986; 63 K Takeuchi (762_CR22) 1977; 29 J Wells (762_CR25) 2020; 208 J Paupert (762_CR20) 2012; 157 GD Mostow (762_CR12) 1980; 86 M Deraux (762_CR4) 2020; 20 M Gromov (762_CR9) 1988; 66 762_CR17 W Couwenberg (762_CR2) 2005; 101 |
| References_xml | – reference: PasquinelliIFundamental domains and presentations for the Deligne-Mostow lattices with 2-fold symmetryPacific J. Math.20193021201247402877210.2140/pjm.2019.302.2011436.22007 – reference: CouwenbergWHeckmanGLooijengaEGeometric structures on the complement of a projective arrangementPubl. Math. Inst. Hautes Études Sci.200510169161221704710.1007/s10240-005-0032-31083.14039 – reference: DelignePMostowGDMonodromy of hypergeometric functions and nonlattice integral monodromyInst. Hautes Études Sci. Publ. Math.19866358984965110.1007/BF028316220615.22008 – reference: GromovMPiatetski-ShapiroINonarithmetic groups in Lobachevsky spacesInst. Hautes Études Sci. Publ. Math.1988669310393213510.1007/BF026989280649.22007 – reference: Parker, John R.: Complex hyperbolic lattices. In Discrete groups and geometric structures, volume 501 of Contemp. Math., pages 1–42. Amer. Math. Soc., Providence, RI, (2009) – reference: DerauxMA new nonarithmetic lattice in PU(3,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm PU}(3,1)$$\end{document}Algebr. Geom. Topol.2020202925963409231510.2140/agt.2020.20.9251457.22003 – reference: Kobayashi, R.: Uniformization of complex surfaces. In: Kähler metric and moduli spaces, volume 18 of Adv. Stud. Pure Math., pp. 313–394. Academic Press, Boston, MA (1990) – reference: MostowGDBraids, hypergeometric functions, and latticesBull. Am. Math. Soc. (N.S.)198716222524687695910.1090/S0273-0979-1987-15510-80639.22005 – reference: YamazakiTYoshidaMOn Hirzebruch’s examples of surfaces with c12=3c2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c^{2}_{1}=3c_{2}$$\end{document}Math. Ann.1984266442143173552510.1007/BF014585370513.14008 – reference: Goldman, W. M.: Complex hyperbolic geometry. In: Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (1999). Oxford Science Publications – reference: DerauxMParkerJRPaupertJNew nonarithmetic complex hyperbolic lattices IIMichigan Math. J.2021701135205425509110.1307/mmj/159253204407390741 – reference: Thurston, William P.: Shapes of polyhedra and triangulations of the sphere. In The Epstein birthday schrift, volume 1 of Geom. Topol. Monogr., pages 511–549. Geom. Topol. Publ., Coventry, (1998) – reference: Paupert, Julien, Wells, Joseph: Hybrid lattices and thin subgroups of picard modular groups. arXiv preprint arXiv:1806.01438, (2019) – reference: Maclachlan, Colin, Reid, Alan W.: The arithmetic of hyperbolic 3-manifolds. Graduate Texts in Mathematics, vol. 219. Springer-Verlag, New York (2003) – reference: PaupertJNon-discrete hybrids in SU(2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm SU}(2,1)$$\end{document}Geom. Dedicata.2012157259268289348810.1007/s10711-011-9609-91271.22008 – reference: WellsJNon-arithmetic hybrid lattices in PU(2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rm PU(2,1)$$\end{document}Geom. Dedicata.2020208111414291310.1007/s10711-019-00506-51441.22023 – reference: Hirzebruch, F.: Arrangements of lines and algebraic surfaces. In: Arithmetic and geometry, Vol. II, volume 36 of Progr. Math., pp. 113–140. Birkhäuser, Boston (1983) – reference: MostowGDOn a remarkable class of polyhedra in complex hyperbolic spacePac. J. Math.198086117127658687610.2140/pjm.1980.86.1710456.22012 – reference: PasquinelliIDeligne-Mostow lattices with three fold symmetry and cone metrics on the sphereConform. Geom. Dyn.201620235281352298310.1090/ecgd/2991354.32014 – reference: Barthel, G., Hirzebruch, F., Höfer, T.: Geradenkonfigurationen und Algebraische Flächen. In: Aspects of Mathematics, D4. Friedr. Vieweg & Sohn, Braunschweig (1987) – reference: Dashyan, R.: A construction of representations of 3-manifold groups into PU(2,1) through Lefschetz fibrations. arXiv:1909.10229 (2019) – reference: DerauxMParkerJRPaupertJNew non-arithmetic complex hyperbolic latticesInvent. Math.20162033681771346136510.1007/s00222-015-0600-11337.22007 – reference: ParkerJRCone metrics on the sphere and Livné’s latticesActa Math.20061961164223720510.1007/s11511-006-0001-91100.57017 – reference: Tretkoff, Paula: Complex ball quotients and line arrangements in the projective plane, volume 51 of Mathematical Notes. Princeton University Press, Princeton, NJ, 2016. With an appendix by Hans-Christoph Im Hof – reference: MostowGDGeneralized Picard lattices arising from half-integral conditionsInst. Hautes Études Sci. Publ. Math.1986639110684965210.1007/BF028316230615.22009 – reference: TakeuchiKArithmetic triangle groupsJ. Math. Soc. Japan19772919110642974410.2969/jmsj/029100910344.20035 – volume: 157 start-page: 259 year: 2012 ident: 762_CR20 publication-title: Geom. Dedicata. doi: 10.1007/s10711-011-9609-9 – volume: 302 start-page: 201 issue: 1 year: 2019 ident: 762_CR19 publication-title: Pacific J. Math. doi: 10.2140/pjm.2019.302.201 – ident: 762_CR17 doi: 10.1090/conm/501/09838 – ident: 762_CR23 doi: 10.2140/gtm.1998.1.511 – ident: 762_CR10 doi: 10.1007/978-1-4757-9286-7_7 – volume: 86 start-page: 171 issue: 1 year: 1980 ident: 762_CR12 publication-title: Pac. J. Math. doi: 10.2140/pjm.1980.86.171 – volume: 66 start-page: 93 year: 1988 ident: 762_CR9 publication-title: Inst. Hautes Études Sci. Publ. Math. doi: 10.1007/BF02698928 – volume: 266 start-page: 421 issue: 4 year: 1984 ident: 762_CR26 publication-title: Math. Ann. doi: 10.1007/BF01458537 – volume: 63 start-page: 91 year: 1986 ident: 762_CR13 publication-title: Inst. Hautes Études Sci. Publ. Math. doi: 10.1007/BF02831623 – volume: 203 start-page: 681 issue: 3 year: 2016 ident: 762_CR6 publication-title: Invent. Math. doi: 10.1007/s00222-015-0600-1 – ident: 762_CR11 doi: 10.1016/B978-0-12-001011-0.50014-2 – volume: 16 start-page: 225 issue: 2 year: 1987 ident: 762_CR14 publication-title: Bull. Am. Math. Soc. (N.S.) doi: 10.1090/S0273-0979-1987-15510-8 – volume: 20 start-page: 235 year: 2016 ident: 762_CR18 publication-title: Conform. Geom. Dyn. doi: 10.1090/ecgd/299 – volume: 101 start-page: 69 year: 2005 ident: 762_CR2 publication-title: Publ. Math. Inst. Hautes Études Sci. doi: 10.1007/s10240-005-0032-3 – ident: 762_CR8 doi: 10.1093/oso/9780198537939.001.0001 – volume: 20 start-page: 925 issue: 2 year: 2020 ident: 762_CR4 publication-title: Algebr. Geom. Topol. doi: 10.2140/agt.2020.20.925 – volume: 70 start-page: 135 issue: 1 year: 2021 ident: 762_CR7 publication-title: Michigan Math. J. doi: 10.1307/mmj/1592532044 – ident: 762_CR3 – ident: 762_CR21 doi: 10.1016/j.topol.2019.106918 – volume: 63 start-page: 5 year: 1986 ident: 762_CR5 publication-title: Inst. Hautes Études Sci. Publ. Math. doi: 10.1007/BF02831622 – ident: 762_CR24 doi: 10.23943/princeton/9780691144771.001.0001 – volume: 208 start-page: 1 year: 2020 ident: 762_CR25 publication-title: Geom. Dedicata. doi: 10.1007/s10711-019-00506-5 – volume: 29 start-page: 91 issue: 1 year: 1977 ident: 762_CR22 publication-title: J. Math. Soc. Japan doi: 10.2969/jmsj/02910091 – volume: 196 start-page: 1 issue: 1 year: 2006 ident: 762_CR16 publication-title: Acta Math. doi: 10.1007/s11511-006-0001-9 – ident: 762_CR15 doi: 10.1007/978-1-4757-6720-9 – ident: 762_CR1 doi: 10.1007/978-3-322-92886-3 |
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| Snippet | A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in... A class of complex hyperbolic lattices in PU (2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [1, 10] and [24]) in terms of... A class of complex hyperbolic lattices in PU(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [1, 10] and [24]) in terms of... |
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| SubjectTerms | Algebraic Geometry Construction Convex and Discrete Geometry Differential Geometry Hyperbolic Geometry Inequality Lattices Mathematics Mathematics and Statistics Original Paper Projective Geometry Quadrilaterals Symmetry Topology |
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