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Article: A Note on Higher Cohomology Groups of Kähler Quotients
Title | A Note on Higher Cohomology Groups of Kähler Quotients |
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Authors | |
Keywords | Geometric Quantization Holomorphic Morse Theory |
Issue Date | 2000 |
Publisher | Springer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0232-704X |
Citation | Annals Of Global Analysis And Geometry, 2000, v. 18 n. 6, p. 569-576 How to Cite? |
Abstract | Consider a holomorphic ℂx-action on a possibly noncompact Kähler manifold. We show that the higher cohomology groups appearing in the geometric quantization of the symplectic quotient are isomorphic to the invariant parts of the corresponding cohomology groups of the original manifold. For non-Abelian group actions on compact Kähler manifolds, this result was proved recently by Teleman. Our approach is applying the holomorphic instanton complex to the prequantum line bundles over the symplectic cuts. We also settle a conjecture of Zhang and the present author on the exact sequence of higher cohomology groups in the context of symplectic cutting. |
Persistent Identifier | http://hdl.handle.net/10722/156111 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.587 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Wu, S | en_US |
dc.date.accessioned | 2012-08-08T08:40:26Z | - |
dc.date.available | 2012-08-08T08:40:26Z | - |
dc.date.issued | 2000 | en_US |
dc.identifier.citation | Annals Of Global Analysis And Geometry, 2000, v. 18 n. 6, p. 569-576 | en_US |
dc.identifier.issn | 0232-704X | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156111 | - |
dc.description.abstract | Consider a holomorphic ℂx-action on a possibly noncompact Kähler manifold. We show that the higher cohomology groups appearing in the geometric quantization of the symplectic quotient are isomorphic to the invariant parts of the corresponding cohomology groups of the original manifold. For non-Abelian group actions on compact Kähler manifolds, this result was proved recently by Teleman. Our approach is applying the holomorphic instanton complex to the prequantum line bundles over the symplectic cuts. We also settle a conjecture of Zhang and the present author on the exact sequence of higher cohomology groups in the context of symplectic cutting. | en_US |
dc.language | eng | en_US |
dc.publisher | Springer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0232-704X | en_US |
dc.relation.ispartof | Annals of Global Analysis and Geometry | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.rights | The original publication is available at www.springerlink.com | - |
dc.subject | Geometric Quantization | en_US |
dc.subject | Holomorphic Morse Theory | en_US |
dc.title | A Note on Higher Cohomology Groups of Kähler Quotients | en_US |
dc.type | Article | en_US |
dc.identifier.email | Wu, S:swu@maths.hku.hk | en_US |
dc.identifier.authority | Wu, S=rp00814 | en_US |
dc.description.nature | preprint | en_US |
dc.identifier.doi | 10.1023/A:1006712005064 | - |
dc.identifier.scopus | eid_2-s2.0-0041727409 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0041727409&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 18 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.spage | 569 | en_US |
dc.identifier.epage | 576 | en_US |
dc.identifier.isi | WOS:000165376300004 | - |
dc.publisher.place | Netherlands | en_US |
dc.identifier.scopusauthorid | Wu, S=15830510400 | en_US |
dc.identifier.issnl | 0232-704X | - |