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Conference Paper: Universal Covering Maps from Bounded Symmetric Domains to Their FiniteVolume Quotients
Title  Universal Covering Maps from Bounded Symmetric Domains to Their FiniteVolume Quotients 

Authors  
Issue Date  2019 
Citation  International conference on Periods and Lfunctions in honor of Gisbert Wüstholz's 70th birthday, Tsinghua Sanya International Mathematics Forum, Sanya, Hainan, China, 2024 January 2019 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 higher dimensions 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 appropriate 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 $pi_Gamma: Omega o X_Gamma$ from a bounded symmetric domain $Omega$ onto its quotient $X_Gamma := Omega/Gamma$ by a torsionfree discrete lattice $Gamma subset {
m Aut}(Omega)$. We will explain an approach from the perspectives of Complex Differential Geometry and Several Complex Variables 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 solutions of various problems from Functional Transcendence Theory concerning totally geodesic subvarieties of finitevolume quotients without the assumption of arithmeticity.

Persistent Identifier  http://hdl.handle.net/10722/269125 
DC Field  Value  Language 

dc.contributor.author  Mok, N   
dc.date.accessioned  20190412T09:53:19Z   
dc.date.available  20190412T09:53:19Z   
dc.date.issued  2019   
dc.identifier.citation  International conference on Periods and Lfunctions in honor of Gisbert Wüstholz's 70th birthday, Tsinghua Sanya International Mathematics Forum, Sanya, Hainan, China, 2024 January 2019   
dc.identifier.uri  http://hdl.handle.net/10722/269125   
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 higher dimensions 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 appropriate 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 $pi_Gamma: Omega o X_Gamma$ from a bounded symmetric domain $Omega$ onto its quotient $X_Gamma := Omega/Gamma$ by a torsionfree discrete lattice $Gamma subset { m Aut}(Omega)$. We will explain an approach from the perspectives of Complex Differential Geometry and Several Complex Variables 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 solutions of various problems from Functional Transcendence Theory concerning totally geodesic subvarieties of finitevolume quotients without the assumption of arithmeticity.   
dc.language  eng   
dc.relation.ispartof  International Conference on Periods and Lfunctions in honor of Gisbert Wüstholz’s 70th birthday, Tsinghua Sanya International Mathematics Forum   
dc.title  Universal Covering Maps from Bounded Symmetric Domains to Their FiniteVolume Quotients   
dc.type  Conference_Paper   
dc.identifier.email  Mok, N: nmok@hku.hk   
dc.identifier.authority  Mok, N=rp00763   
dc.identifier.hkuros  296726   