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Article: Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds

TitleAnalytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds
Authors
Issue Date2010
PublisherLehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.html
Citation
Journal Of Differential Geometry, 2010, v. 86 n. 3, p. 539-567 How to Cite?
AbstractIn a series of works, one of the authors has developed with J.-M. Hwang a geometric theory of uniruled projective manifolds, especially those of Picard number 1, basing on the study of varieties of minimal rational tangents. A fundamental result in this theory is a principle of analytic continuation under very mild assumptions, called Cartan-Fubini extension, of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents. In this article we develop a generalization of Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends varieties of minimal rational tangents onto linear sections of varieties of minimal rational tangents and that it satisfies a mild geometric condition formulated in terms of second fundamental forms on varieties of minimal rational tangents. Formerly such a result was known only in the very special case of irreducible Hermitian symmetric manifolds of rank at least two, and the proof relied on the existence of flattening coordinates, viz., Harish-Chandra coordinates, with respect to which the varieties of minimal rational tangents form a constant family. The proof of the main result, which is based on the deformation theory of rational curves, is differential-geometric in nature and is applicable to the general situation of uniruled projective manifolds without any assumption on the existence of special coordinate systems. As an application, we give a characterization of standard embeddings for certain pairs of rational homogeneous manifolds in terms of embeddings of varieties of minimal rational tangents.
Persistent Identifierhttp://hdl.handle.net/10722/135148
ISSN
2015 Impact Factor: 1.24
2015 SCImago Journal Rankings: 3.244
References

 

DC FieldValueLanguage
dc.contributor.authorHong, Jen_HK
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2011-07-27T01:29:07Z-
dc.date.available2011-07-27T01:29:07Z-
dc.date.issued2010en_HK
dc.identifier.citationJournal Of Differential Geometry, 2010, v. 86 n. 3, p. 539-567en_HK
dc.identifier.issn0022-040Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/135148-
dc.description.abstractIn a series of works, one of the authors has developed with J.-M. Hwang a geometric theory of uniruled projective manifolds, especially those of Picard number 1, basing on the study of varieties of minimal rational tangents. A fundamental result in this theory is a principle of analytic continuation under very mild assumptions, called Cartan-Fubini extension, of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents. In this article we develop a generalization of Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends varieties of minimal rational tangents onto linear sections of varieties of minimal rational tangents and that it satisfies a mild geometric condition formulated in terms of second fundamental forms on varieties of minimal rational tangents. Formerly such a result was known only in the very special case of irreducible Hermitian symmetric manifolds of rank at least two, and the proof relied on the existence of flattening coordinates, viz., Harish-Chandra coordinates, with respect to which the varieties of minimal rational tangents form a constant family. The proof of the main result, which is based on the deformation theory of rational curves, is differential-geometric in nature and is applicable to the general situation of uniruled projective manifolds without any assumption on the existence of special coordinate systems. As an application, we give a characterization of standard embeddings for certain pairs of rational homogeneous manifolds in terms of embeddings of varieties of minimal rational tangents.en_HK
dc.languageengen_US
dc.publisherLehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.htmlen_HK
dc.relation.ispartofJournal of Differential Geometryen_HK
dc.titleAnalytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifoldsen_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-s2.0-79953323687en_HK
dc.identifier.hkuros186042en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79953323687&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume86en_HK
dc.identifier.issue3en_HK
dc.identifier.spage539en_HK
dc.identifier.epage567en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridHong, J=15750365300en_HK
dc.identifier.scopusauthoridMok, N=7004348032en_HK

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