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Article: Nonexistence of holomorphic submersions between complex unit balls equivariant with respect to a lattice and their generalizations
Title  Nonexistence of holomorphic submersions between complex unit balls equivariant with respect to a lattice and their generalizations 

Authors  
Issue Date  2010 
Publisher  The Johns Hopkins University Press. The Journal's web site is located at http://www.press.jhu.edu/journals/american_journal_of_mathematics/index.html 
Citation  American Journal Of Mathematics, 2010, v. 132 n. 5, p. 13471363 How to Cite? 
Abstract  In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a nonequidimensional surjective holomorphic map between compact ball quotients, our method applies to show that the set of critical values must be nonempty and of codimension 1. In the equivariant setting the line of arguments extends to holomorphic mappings of maximal rank into the complex projective space or the complex Euclidean space, yielding in the latter case a lower bound on the dimension of the singular loci of certain holomorphic maps defined by integrating holomorphic 1forms. In another direction, we extend the nonexistence statement on holomorphic submersions to the case of ball quotients of finite volume, provided that the target complex unit ball is of dimension m > 2, giving in particular a new proof that a local biholomorphism between noncompact mball quotients of finite volume must be a covering map whenever m > 2. Finally, combining our results with Hermitian metric rigidity, we show that any holomorphic submersion from a bounded symmetric domain into a complex unit ball equivariant with respect to a lattice must factor through a canonical projection to yield an automorphism of the complex unit ball, provided that either the lattice is cocompact or the ball is of dimension at least 2. © 2010 by The Johns Hopkins University Press. 
Persistent Identifier  http://hdl.handle.net/10722/135147 
ISSN  2015 Impact Factor: 1.118 2015 SCImago Journal Rankings: 3.513 
References 
DC Field  Value  Language 

dc.contributor.author  Koziarz, V  en_HK 
dc.contributor.author  Mok, N  en_HK 
dc.date.accessioned  20110727T01:29:06Z   
dc.date.available  20110727T01:29:06Z   
dc.date.issued  2010  en_HK 
dc.identifier.citation  American Journal Of Mathematics, 2010, v. 132 n. 5, p. 13471363  en_HK 
dc.identifier.issn  00029327  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/135147   
dc.description.abstract  In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a nonequidimensional surjective holomorphic map between compact ball quotients, our method applies to show that the set of critical values must be nonempty and of codimension 1. In the equivariant setting the line of arguments extends to holomorphic mappings of maximal rank into the complex projective space or the complex Euclidean space, yielding in the latter case a lower bound on the dimension of the singular loci of certain holomorphic maps defined by integrating holomorphic 1forms. In another direction, we extend the nonexistence statement on holomorphic submersions to the case of ball quotients of finite volume, provided that the target complex unit ball is of dimension m > 2, giving in particular a new proof that a local biholomorphism between noncompact mball quotients of finite volume must be a covering map whenever m > 2. Finally, combining our results with Hermitian metric rigidity, we show that any holomorphic submersion from a bounded symmetric domain into a complex unit ball equivariant with respect to a lattice must factor through a canonical projection to yield an automorphism of the complex unit ball, provided that either the lattice is cocompact or the ball is of dimension at least 2. © 2010 by The Johns Hopkins University Press.  en_HK 
dc.language  eng  en_US 
dc.publisher  The Johns Hopkins University Press. The Journal's web site is located at http://www.press.jhu.edu/journals/american_journal_of_mathematics/index.html  en_HK 
dc.relation.ispartof  American Journal of Mathematics  en_HK 
dc.title  Nonexistence of holomorphic submersions between complex unit balls equivariant with respect to a lattice and their generalizations  en_HK 
dc.type  Article  en_HK 
dc.identifier.email  Mok, N:nmok@hkucc.hku.hk  en_HK 
dc.identifier.authority  Mok, N=rp00763  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.doi  10.1353/ajm.2010.0007  en_HK 
dc.identifier.scopus  eid_2s2.077958584042  en_HK 
dc.identifier.hkuros  186040  en_US 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.077958584042&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  132  en_HK 
dc.identifier.issue  5  en_HK 
dc.identifier.spage  1347  en_HK 
dc.identifier.epage  1363  en_HK 
dc.identifier.eissn  10806377   
dc.publisher.place  United States  en_HK 
dc.identifier.scopusauthorid  Koziarz, V=8352624600  en_HK 
dc.identifier.scopusauthorid  Mok, N=7004348032  en_HK 