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Conference Paper: Uniformization of Subvarieties of FiniteVolume Quotient Spaces of Bounded Symmetric Domains
Title  Uniformization of Subvarieties of FiniteVolume Quotient Spaces of Bounded Symmetric Domains 

Authors  
Issue Date  2019 
Citation  Topics on Nevanlinna Theory and Complex Hyperbolicities Conference, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China, 2527 July 2019 How to Cite? 
Abstract  The Siegel upper half plane Hg belongs, up to biholomorphic equivalence, to the set of bounded symmetricdomains, on which a great deal of mathematical research is taking place. Especially, finitevolume quotients of bounded symmetric domains, which are naturally quasiprojective varieties, are objects of immense interest to Several Complex Variables, Algebraic Geometry, Arithmetic Geometry and Number Theory, and an important topic is the study of covering spaces of algebraic subsets of such quasiprojective varieties. While a lot has already been achieved in the case of Shimura varieties by means of methods of Diophantine Geometry, Model Theory, Hodge Theory and Complex Differential Geometry, techniques for the general case of not necessarily arithmetic quotients =ΩΓ⁄have just begun to be developed. For instance, uniformization problems for subvarieties of products of arbitrary compact Riemann surfaces of genus ≥2 have hitherto been untractable by existing methods. We will explain a differentialgeometric approach leading to various characterization results for totally geodesic subvarieties of finitevolume quotients =ΩΓ⁄. Especially, we will explain how the study of holomorphic isometric embeddings of the Poincare disk and more generally complex unit balls into bounded symmetric domains can be further developed to derive uniformization theorems for bialgebraic varieties and more generally for the Zariski closure of images of algebraic sets under the universal covering map. 
Persistent Identifier  http://hdl.handle.net/10722/297760 
DC Field  Value  Language 

dc.contributor.author  Mok, N   
dc.date.accessioned  20210329T09:50:25Z   
dc.date.available  20210329T09:50:25Z   
dc.date.issued  2019   
dc.identifier.citation  Topics on Nevanlinna Theory and Complex Hyperbolicities Conference, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China, 2527 July 2019   
dc.identifier.uri  http://hdl.handle.net/10722/297760   
dc.description.abstract  The Siegel upper half plane Hg belongs, up to biholomorphic equivalence, to the set of bounded symmetricdomains, on which a great deal of mathematical research is taking place. Especially, finitevolume quotients of bounded symmetric domains, which are naturally quasiprojective varieties, are objects of immense interest to Several Complex Variables, Algebraic Geometry, Arithmetic Geometry and Number Theory, and an important topic is the study of covering spaces of algebraic subsets of such quasiprojective varieties. While a lot has already been achieved in the case of Shimura varieties by means of methods of Diophantine Geometry, Model Theory, Hodge Theory and Complex Differential Geometry, techniques for the general case of not necessarily arithmetic quotients =ΩΓ⁄have just begun to be developed. For instance, uniformization problems for subvarieties of products of arbitrary compact Riemann surfaces of genus ≥2 have hitherto been untractable by existing methods. We will explain a differentialgeometric approach leading to various characterization results for totally geodesic subvarieties of finitevolume quotients =ΩΓ⁄. Especially, we will explain how the study of holomorphic isometric embeddings of the Poincare disk and more generally complex unit balls into bounded symmetric domains can be further developed to derive uniformization theorems for bialgebraic varieties and more generally for the Zariski closure of images of algebraic sets under the universal covering map.   
dc.language  eng   
dc.relation.ispartof  Topics on Nevanlinna Theory and Complex Hyperbolicities Conference, Shanghai Center for Mathematical Sciences, Fudan University,   
dc.title  Uniformization of Subvarieties of FiniteVolume Quotient Spaces of Bounded Symmetric Domains   
dc.type  Conference_Paper   
dc.identifier.email  Mok, N: nmok@hku.hk   
dc.identifier.authority  Mok, N=rp00763   
dc.identifier.hkuros  301587   