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Book Chapter: Projective Algebraicity of Minimal Compactifications of ComplexHyperbolic Space Forms of Finite Volume
Title  Projective Algebraicity of Minimal Compactifications of ComplexHyperbolic Space Forms of Finite Volume 

Authors  
Issue Date  2012 
Publisher  Birkhäuser Springer 
Citation  Projective Algebraicity of Minimal Compactifications of ComplexHyperbolic Space Forms of Finite Volume. In Itenberg, I., Jöricke, B & Passare, M (Eds.), Perspectives in analysis, geometry, and topology: on the occasion of the 60th birthday of Oleg Viro, p. 331354. New York: Birkhäuser Springer, 2012 How to Cite? 
Abstract  Let Ωbe a bounded symmetric domain and Γ⊂ Aut(Ω) be an irreducible nonuniform torsionfree discrete subgroup. When Γis of rank ≥ 2, Γis necessarily arithmetic, and X :=Ω/Γ?admits a SatakeBailyBorel compactification. When Ω?is of rank 1, i.e., the complex unit ball Bn of dimension n≥ 1,Γmay be nonarithmetic.When n≥2, by a general result of Siu and Yau, X is pseudoconcave and it can be compactified to a Moishezon space by adding a finite number of normal isolated singularities. In this article we show that for X := Bn/Γ the latter compactification is in fact projectivealgebraic.We do this by showing that, just as in the arithmetic case of rank1, X admits a smooth toroidal compactification X¯ M obtained by adjoining an Abelian variety to each of its finitely many ends, and X¯ M can be blown down to a normal projectivealgebraic variety X¯ Min by solving ∂¯ with L2estimates with respect to the canonical KählerEinstein metric and by normalization. As an application, we give an alternative proof of results of KoziarzMok on the submersion problem in the case of complexhyperbolic space forms of finite volume by adapting the cohomological arguments in the compact case to general hyperplane sections of the minimal projectivealgebraic compactifications which avoid the isolated singularities. 
Persistent Identifier  http://hdl.handle.net/10722/187440 
ISBN  
ISI Accession Number ID  
Series/Report no.  Progress in mathematics; v.296 
DC Field  Value  Language 

dc.contributor.author  Mok, N  en_US 
dc.date.accessioned  20130820T12:45:18Z   
dc.date.available  20130820T12:45:18Z   
dc.date.issued  2012  en_US 
dc.identifier.citation  Projective Algebraicity of Minimal Compactifications of ComplexHyperbolic Space Forms of Finite Volume. In Itenberg, I., Jöricke, B & Passare, M (Eds.), Perspectives in analysis, geometry, and topology: on the occasion of the 60th birthday of Oleg Viro, p. 331354. New York: Birkhäuser Springer, 2012  en_US 
dc.identifier.isbn  9780817682767   
dc.identifier.uri  http://hdl.handle.net/10722/187440   
dc.description.abstract  Let Ωbe a bounded symmetric domain and Γ⊂ Aut(Ω) be an irreducible nonuniform torsionfree discrete subgroup. When Γis of rank ≥ 2, Γis necessarily arithmetic, and X :=Ω/Γ?admits a SatakeBailyBorel compactification. When Ω?is of rank 1, i.e., the complex unit ball Bn of dimension n≥ 1,Γmay be nonarithmetic.When n≥2, by a general result of Siu and Yau, X is pseudoconcave and it can be compactified to a Moishezon space by adding a finite number of normal isolated singularities. In this article we show that for X := Bn/Γ the latter compactification is in fact projectivealgebraic.We do this by showing that, just as in the arithmetic case of rank1, X admits a smooth toroidal compactification X¯ M obtained by adjoining an Abelian variety to each of its finitely many ends, and X¯ M can be blown down to a normal projectivealgebraic variety X¯ Min by solving ∂¯ with L2estimates with respect to the canonical KählerEinstein metric and by normalization. As an application, we give an alternative proof of results of KoziarzMok on the submersion problem in the case of complexhyperbolic space forms of finite volume by adapting the cohomological arguments in the compact case to general hyperplane sections of the minimal projectivealgebraic compactifications which avoid the isolated singularities.   
dc.language  eng  en_US 
dc.publisher  Birkhäuser Springer  en_US 
dc.relation.ispartof  Perspectives in analysis, geometry, and topology: on the occasion of the 60th birthday of Oleg Viro   
dc.relation.ispartofseries  Progress in mathematics; v.296   
dc.title  Projective Algebraicity of Minimal Compactifications of ComplexHyperbolic Space Forms of Finite Volume  en_US 
dc.type  Book_Chapter  en_US 
dc.identifier.email  Mok, N: nmok@hku.hk  en_US 
dc.identifier.authority  Mok, N=rp00763  en_US 
dc.identifier.doi  10.1007/9780817682774_14   
dc.identifier.hkuros  217113  en_US 
dc.identifier.spage  331  en_US 
dc.identifier.epage  354  en_US 
dc.identifier.isi  WOS:000307264800015   
dc.publisher.place  New York  en_US 