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Conference Paper: Universal Covering Maps onto FiniteVolume Quotients of Bounded Symmetric Domains from the Perspective of Complex Differential Geometry
Title  Universal Covering Maps onto FiniteVolume Quotients of Bounded Symmetric Domains from the Perspective of Complex Differential Geometry 

Authors  
Issue Date  2018 
Citation  The 24th Symposium on Complex Geometry, Kanazawa, Japan, 1316 November 2018 How to Cite? 
Abstract  By the Uniformization Theorem a compact Riemann surface other than the Riemann Sphere or an elliptic curve is uniformized by the unit disk and equivalently by the upper half plane. The upper half plane is also the universal covering space of the moduli space of elliptic curves equipped with a suitable level structure. In Several Complex Variables, the Siegel upper half plane (which is biholomorphic to a bounded symmetric domain) is an analogue of the upper half plane, and it is the universal covering space of moduli spaces of polarized Abelian varieties with level structures. In general, finitevolume quotients of bounded symmetric domains, which are naturally quasiprojective varieties, are of immense interest to Several Complex Variables, Algebraic Geometry and Number Theory, and an important object of study is the universal covering map πΓ : Ω → XΓ from a bounded symmetric domain Ω onto its quotient XΓ := Ω/Γ by a torsionfree discrete lattice Γ ⊂ Aut(Ω). We will explain a differentialgeometric approach to the study of the universal covering map revolving around the notion of asymptotic curvature behavior, rescaling arguments and the use of meromorphic foliations, and illustrate how this approach using transcendental techniques leads to various results concerning totally geodesic subvarieties of finitevolume quotients without the assumption of arithmeticity. 
Persistent Identifier  http://hdl.handle.net/10722/269055 
DC Field  Value  Language 

dc.contributor.author  Mok, N   
dc.date.accessioned  20190410T08:34:24Z   
dc.date.available  20190410T08:34:24Z   
dc.date.issued  2018   
dc.identifier.citation  The 24th Symposium on Complex Geometry, Kanazawa, Japan, 1316 November 2018   
dc.identifier.uri  http://hdl.handle.net/10722/269055   
dc.description.abstract  By the Uniformization Theorem a compact Riemann surface other than the Riemann Sphere or an elliptic curve is uniformized by the unit disk and equivalently by the upper half plane. The upper half plane is also the universal covering space of the moduli space of elliptic curves equipped with a suitable level structure. In Several Complex Variables, the Siegel upper half plane (which is biholomorphic to a bounded symmetric domain) is an analogue of the upper half plane, and it is the universal covering space of moduli spaces of polarized Abelian varieties with level structures. In general, finitevolume quotients of bounded symmetric domains, which are naturally quasiprojective varieties, are of immense interest to Several Complex Variables, Algebraic Geometry and Number Theory, and an important object of study is the universal covering map πΓ : Ω → XΓ from a bounded symmetric domain Ω onto its quotient XΓ := Ω/Γ by a torsionfree discrete lattice Γ ⊂ Aut(Ω). We will explain a differentialgeometric approach to the study of the universal covering map revolving around the notion of asymptotic curvature behavior, rescaling arguments and the use of meromorphic foliations, and illustrate how this approach using transcendental techniques leads to various results concerning totally geodesic subvarieties of finitevolume quotients without the assumption of arithmeticity.   
dc.language  eng   
dc.relation.ispartof  The 24th Symposium on Complex Geometry, 2018   
dc.title  Universal Covering Maps onto FiniteVolume Quotients of Bounded Symmetric Domains from the Perspective of Complex Differential Geometry   
dc.type  Conference_Paper   
dc.identifier.email  Mok, N: nmok@hku.hk   
dc.identifier.authority  Mok, N=rp00763   
dc.identifier.hkuros  296166   