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Book Chapter: Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds
Title  Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds 

Authors  
Issue Date  2014 
Publisher  World Scientific 
Citation  Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds. In Ge, ML ... (et al) (Eds.), Frontiers in differential geometry, partial differential equations and mathematical physics: in memory of Gu Chaohao, p. 271289. Singapore; New Jersey: World Scientific, 2014 How to Cite? 
Abstract  A complex manifold is said to be a Bergman manifold if the Bergman kernel form induces in the standard way a Kähler metric on the manifold. A Bergman manifold is said to be canonically embeddable if the canonical map into a possibly infinitedimensional projective space defined using the Hilbert space of squareintegrable holomorphic nforms is a holomorphic embedding. In this article we define for a canonically embeddable Bergman manifold X the notion of Bergman meromorphic compactifications i: X ↪ Z into compact complex manifolds Z characterized in terms of extension properties concerning the Bergman kernel form on X, and define the notion of minimal elements among such compactifications. We prove that such a compact complex manifold Z is necessarily Moishezon. When X is given, assuming the existence of Bergman meromorphic compactifications i: X ↪ Z we prove the existence of a minimal element among them. More precisely, starting with any Bergman meromorphic compactification i: X ↪ Z we construct reductions of the compactification, and show that any reduction necessarily defines a minimal element. We show that up to a certain natural equivalence relation the minimal Bergman meromorphic compactification is unique. Examples of such compactifications include Borel embeddings of bounded symmetric domains into their compact dual manifolds and also those arising from canonical realizations of bounded homogeneous domains as Siegel domains or as bounded domains on Euclidean spaces and hence as domains on projective spaces. 
Persistent Identifier  http://hdl.handle.net/10722/205255 
ISBN 
DC Field  Value  Language 

dc.contributor.author  Mok, N  en_US 
dc.date.accessioned  20140920T02:07:07Z   
dc.date.available  20140920T02:07:07Z   
dc.date.issued  2014  en_US 
dc.identifier.citation  Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds. In Ge, ML ... (et al) (Eds.), Frontiers in differential geometry, partial differential equations and mathematical physics: in memory of Gu Chaohao, p. 271289. Singapore; New Jersey: World Scientific, 2014  en_US 
dc.identifier.isbn  9789814578073   
dc.identifier.uri  http://hdl.handle.net/10722/205255   
dc.description.abstract  A complex manifold is said to be a Bergman manifold if the Bergman kernel form induces in the standard way a Kähler metric on the manifold. A Bergman manifold is said to be canonically embeddable if the canonical map into a possibly infinitedimensional projective space defined using the Hilbert space of squareintegrable holomorphic nforms is a holomorphic embedding. In this article we define for a canonically embeddable Bergman manifold X the notion of Bergman meromorphic compactifications i: X ↪ Z into compact complex manifolds Z characterized in terms of extension properties concerning the Bergman kernel form on X, and define the notion of minimal elements among such compactifications. We prove that such a compact complex manifold Z is necessarily Moishezon. When X is given, assuming the existence of Bergman meromorphic compactifications i: X ↪ Z we prove the existence of a minimal element among them. More precisely, starting with any Bergman meromorphic compactification i: X ↪ Z we construct reductions of the compactification, and show that any reduction necessarily defines a minimal element. We show that up to a certain natural equivalence relation the minimal Bergman meromorphic compactification is unique. Examples of such compactifications include Borel embeddings of bounded symmetric domains into their compact dual manifolds and also those arising from canonical realizations of bounded homogeneous domains as Siegel domains or as bounded domains on Euclidean spaces and hence as domains on projective spaces.   
dc.language  eng  en_US 
dc.publisher  World Scientific  en_US 
dc.relation.ispartof  Frontiers in differential geometry, partial differential equations and mathematical physics: in memory of Gu Chaohao   
dc.title  Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds  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  10.1142/9789814578097_0017  en_US 
dc.identifier.hkuros  237309  en_US 
dc.identifier.spage  271  en_US 
dc.identifier.epage  289  en_US 
dc.publisher.place  Singapore; New Jersey  en_US 