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Article: Equivariant holomorphic morse inequalities II: Torus and non-Abelian group actions

TitleEquivariant holomorphic morse inequalities II: Torus and non-Abelian group actions
Authors
Issue Date1999
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, 1999, v. 51 n. 3, p. 401-429 How to Cite?
AbstractWe extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kähler manifolds and show the necessity of the Kähler condition. For torus actions, there is a set of inequalities for each choice of action chambers specifying directions in the Lie algebra of the torus. We apply the results to invariant line bundles over toric manifolds. If the group is non-Abelian, there is in addition an action of the Weyl group on the fixed-point set of its maximal torus. The sum over the fixed points can be rearranged into sums over the Weyl group (having incorporated the character of the isotropy representation on the fiber) and over the orbits of the Weyl group in the fixed-point set.
Persistent Identifierhttp://hdl.handle.net/10722/156094
ISSN
2015 Impact Factor: 1.24
2015 SCImago Journal Rankings: 3.244
References

 

DC FieldValueLanguage
dc.contributor.authorWu, Sen_US
dc.date.accessioned2012-08-08T08:40:23Z-
dc.date.available2012-08-08T08:40:23Z-
dc.date.issued1999en_US
dc.identifier.citationJournal Of Differential Geometry, 1999, v. 51 n. 3, p. 401-429en_US
dc.identifier.issn0022-040Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156094-
dc.description.abstractWe extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kähler manifolds and show the necessity of the Kähler condition. For torus actions, there is a set of inequalities for each choice of action chambers specifying directions in the Lie algebra of the torus. We apply the results to invariant line bundles over toric manifolds. If the group is non-Abelian, there is in addition an action of the Weyl group on the fixed-point set of its maximal torus. The sum over the fixed points can be rearranged into sums over the Weyl group (having incorporated the character of the isotropy representation on the fiber) and over the orbits of the Weyl group in the fixed-point set.en_US
dc.languageengen_US
dc.publisherLehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.htmlen_US
dc.relation.ispartofJournal of Differential Geometryen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleEquivariant holomorphic morse inequalities II: Torus and non-Abelian group actionsen_US
dc.typeArticleen_US
dc.identifier.emailWu, S:swu@maths.hku.hken_US
dc.identifier.authorityWu, S=rp00814en_US
dc.description.naturepostprinten_US
dc.identifier.scopuseid_2-s2.0-0038853073en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0038853073&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume51en_US
dc.identifier.issue3en_US
dc.identifier.spage401en_US
dc.identifier.epage429en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridWu, S=15830510400en_US

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