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

TitleFinite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles
Authors
KeywordsMathematics
Issue Date2003
PublisherAmerican Mathematical Society.
Citation
Journal Of Algebraic Geometry, 2003, v. 12 n. 4, p. 627-651 How to Cite?
AbstractLet 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), 563-575) 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 3-dimensional Fano manifold of Picard number 1 can only dominate a finite number of isomorphism classes of projective manifolds.
Persistent Identifierhttp://hdl.handle.net/10722/42125
ISSN
2015 Impact Factor: 1.191
2015 SCImago Journal Rankings: 2.948
References

 

DC FieldValueLanguage
dc.contributor.authorHwang, JMen_HK
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2007-01-08T02:29:41Z-
dc.date.available2007-01-08T02:29:41Z-
dc.date.issued2003en_HK
dc.identifier.citationJournal Of Algebraic Geometry, 2003, v. 12 n. 4, p. 627-651en_HK
dc.identifier.issn1056-3911en_HK
dc.identifier.urihttp://hdl.handle.net/10722/42125-
dc.description.abstractLet 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), 563-575) 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 3-dimensional 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.publisherAmerican Mathematical Society.en_HK
dc.relation.ispartofJournal of Algebraic Geometryen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsFirst published in Journal of Algebraic Geometry in v. 12, 2003, published by the American Mathematical Societyen_HK
dc.subjectMathematicsen_HK
dc.titleFinite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundlesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1056-3911&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+bundlesen_HK
dc.identifier.emailMok, N:nmok@hkucc.hku.hken_HK
dc.identifier.authorityMok, N=rp00763en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-0141462771en_HK
dc.identifier.hkuros76710-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0141462771&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume12en_HK
dc.identifier.issue4en_HK
dc.identifier.spage627en_HK
dc.identifier.epage651en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridHwang, JM=7403895554en_HK
dc.identifier.scopusauthoridMok, N=7004348032en_HK

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