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Article: Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles
Title  Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles 

Authors  
Keywords  Mathematics 
Issue Date  2003 
Publisher  American Mathematical Society. 
Citation  Journal Of Algebraic Geometry, 2003, v. 12 n. 4, p. 627651 How to Cite? 
Abstract  Let X be a Fano manifold of Picard number 1 admitting a rational curve with trivial normal bundle and f : X′ → X be a generically finite surjective holomorphic map from a projective manifold X′ onto X. When the domain manifold X′ is fixed and the target manifold X is a priori allowed to deform we prove that the holomorphic map f : X′ → X is locally rigid up to biholomorphisms of target manifolds. This result complements, with a completely different method of proof, an earlier local rigidity theorem of ours (see J. Math. Pures Appl. 80 (2001), 563575) for the analogous situation where the target manifold X is a Fano manifold of Picard number 1 on which there is no rational curve with trivial normal bundle. In another direction, given a Fano manifold X′ of Picard number 1, we prove a finiteness result for generically finite surjective holomorphic maps of X′ onto Fano manifolds (necessarily of Picard number 1) admitting rational curves with trivial normal bundles. As a consequence, any 3dimensional Fano manifold of Picard number 1 can only dominate a finite number of isomorphism classes of projective manifolds. 
Persistent Identifier  http://hdl.handle.net/10722/42125 
ISSN  2015 Impact Factor: 1.191 2015 SCImago Journal Rankings: 2.948 
References 
DC Field  Value  Language 

dc.contributor.author  Hwang, JM  en_HK 
dc.contributor.author  Mok, N  en_HK 
dc.date.accessioned  20070108T02:29:41Z   
dc.date.available  20070108T02:29:41Z   
dc.date.issued  2003  en_HK 
dc.identifier.citation  Journal Of Algebraic Geometry, 2003, v. 12 n. 4, p. 627651  en_HK 
dc.identifier.issn  10563911  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/42125   
dc.description.abstract  Let X be a Fano manifold of Picard number 1 admitting a rational curve with trivial normal bundle and f : X′ → X be a generically finite surjective holomorphic map from a projective manifold X′ onto X. When the domain manifold X′ is fixed and the target manifold X is a priori allowed to deform we prove that the holomorphic map f : X′ → X is locally rigid up to biholomorphisms of target manifolds. This result complements, with a completely different method of proof, an earlier local rigidity theorem of ours (see J. Math. Pures Appl. 80 (2001), 563575) for the analogous situation where the target manifold X is a Fano manifold of Picard number 1 on which there is no rational curve with trivial normal bundle. In another direction, given a Fano manifold X′ of Picard number 1, we prove a finiteness result for generically finite surjective holomorphic maps of X′ onto Fano manifolds (necessarily of Picard number 1) admitting rational curves with trivial normal bundles. As a consequence, any 3dimensional Fano manifold of Picard number 1 can only dominate a finite number of isomorphism classes of projective manifolds.  en_HK 
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dc.format.extent  26624 bytes   
dc.format.extent  766772 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  application/msword   
dc.format.mimetype  application/pdf   
dc.publisher  American Mathematical Society.  en_HK 
dc.relation.ispartof  Journal of Algebraic Geometry  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.rights  First published in Journal of Algebraic Geometry in v. 12, 2003, published by the American Mathematical Society  en_HK 
dc.subject  Mathematics  en_HK 
dc.title  Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=10563911&volume=12&issue=4&spage=627&epage=651&date=2003&atitle=Finite+morphisms+onto+Fano+manifolds+of+Picard+number+1+which+have+rational+curves+with+trivial+normal+bundles  en_HK 
dc.identifier.email  Mok, N:nmok@hkucc.hku.hk  en_HK 
dc.identifier.authority  Mok, N=rp00763  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.scopus  eid_2s2.00141462771  en_HK 
dc.identifier.hkuros  76710   
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.00141462771&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  12  en_HK 
dc.identifier.issue  4  en_HK 
dc.identifier.spage  627  en_HK 
dc.identifier.epage  651  en_HK 
dc.publisher.place  United States  en_HK 
dc.identifier.scopusauthorid  Hwang, JM=7403895554  en_HK 
dc.identifier.scopusauthorid  Mok, N=7004348032  en_HK 