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Article: Geometric structures on uniruled projective manifolds defined by their varieties of minimal rational tangents

TitleGeometric structures on uniruled projective manifolds defined by their varieties of minimal rational tangents
Authors
KeywordsAnalytic continuation
Cauchy characteristic
Curvature
Deformation rigidity
Differential system
Distribution
Geometric structure
Minimal rational curve
Nef tangent bundle
Parallel transport
Prolongation
Tangent map
Variety of minimal rational tangents
Issue Date2008
PublisherSociete Mathematique de France. The Journal's web site is located at http://smf4.emath.fr/Publications/Asterisque/
Citation
Asterisque, 2008 n. 322, p. 151-205 How to Cite?
AbstractIn a joint research programme with Jun-Muk Hwang we have been investigating geometric structures on uniruled projective manifolds, especially Fano manifolds of Picard number 1, defined by varieties of minimal rational tangents associated to moduli spaces of minimal rational curves. In this article we outline a heuristic picture of the geometry of Fano manifolds of Picard number 1 with non-linear varieties of minimal rational tangents, taking as hints from prototypical examples such as those from holomorphic conformal structures. On an open set in the complex topology the local geometric structure associated to varieties of minimal rational tangents is equivalently given by families of local holomorphic curves marked at a variable base point satisfying certain compatibility conditions. Differential-geometric notions such as (null) geodesics, curvature and parallel transport are a source of inspiration in our study. Formulation of problems suggested by this heuristic analogy and their solutions, sometimes in a very general context and at other times applicable only to special classes of Fano manifolds, have led to resolutions of a series of well-known problems in Algebraic Geometry. © Astérisque 322.
Persistent Identifierhttp://hdl.handle.net/10722/58946
ISSN
2015 Impact Factor: 0.627
2015 SCImago Journal Rankings: 0.668
References

 

DC FieldValueLanguage
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2010-05-31T03:40:09Z-
dc.date.available2010-05-31T03:40:09Z-
dc.date.issued2008en_HK
dc.identifier.citationAsterisque, 2008 n. 322, p. 151-205en_HK
dc.identifier.issn0303-1179en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58946-
dc.description.abstractIn a joint research programme with Jun-Muk Hwang we have been investigating geometric structures on uniruled projective manifolds, especially Fano manifolds of Picard number 1, defined by varieties of minimal rational tangents associated to moduli spaces of minimal rational curves. In this article we outline a heuristic picture of the geometry of Fano manifolds of Picard number 1 with non-linear varieties of minimal rational tangents, taking as hints from prototypical examples such as those from holomorphic conformal structures. On an open set in the complex topology the local geometric structure associated to varieties of minimal rational tangents is equivalently given by families of local holomorphic curves marked at a variable base point satisfying certain compatibility conditions. Differential-geometric notions such as (null) geodesics, curvature and parallel transport are a source of inspiration in our study. Formulation of problems suggested by this heuristic analogy and their solutions, sometimes in a very general context and at other times applicable only to special classes of Fano manifolds, have led to resolutions of a series of well-known problems in Algebraic Geometry. © Astérisque 322.en_HK
dc.languageengen_HK
dc.publisherSociete Mathematique de France. The Journal's web site is located at http://smf4.emath.fr/Publications/Asterisque/en_HK
dc.relation.ispartofAsterisqueen_HK
dc.subjectAnalytic continuationen_HK
dc.subjectCauchy characteristicen_HK
dc.subjectCurvatureen_HK
dc.subjectDeformation rigidityen_HK
dc.subjectDifferential systemen_HK
dc.subjectDistributionen_HK
dc.subjectGeometric structureen_HK
dc.subjectMinimal rational curveen_HK
dc.subjectNef tangent bundleen_HK
dc.subjectParallel transporten_HK
dc.subjectProlongationen_HK
dc.subjectTangent mapen_HK
dc.subjectVariety of minimal rational tangentsen_HK
dc.titleGeometric structures on uniruled projective manifolds defined by their varieties of minimal rational tangentsen_HK
dc.typeArticleen_HK
dc.identifier.emailMok, N:nmok@hkucc.hku.hken_HK
dc.identifier.authorityMok, N=rp00763en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-66249121401en_HK
dc.identifier.hkuros155540en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-66249121401&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.issue322en_HK
dc.identifier.spage151en_HK
dc.identifier.epage205en_HK
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridMok, N=7004348032en_HK

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