Holomorphic koszulBrylinski homology

Mathieu Stiénon

doi:10.1093/imrn/rnq084

Holomorphic koszulBrylinski homology

Mathieu Stiénon

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

In this note, we study the KoszulBrylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on KoszulBrylinski homology is nondegenerate. Finally, we compute the oszul-Brylinski homology for Poisson structures on ℂℙ¹ × ℂℙ¹.

Original language	English (US)
Pages (from-to)	553-571
Number of pages	19
Journal	International Mathematics Research Notices
Volume	2011
Issue number	3
DOIs	https://doi.org/10.1093/imrn/rnq084
State	Published - 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnq084

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title = "Holomorphic koszulBrylinski homology",

abstract = "In this note, we study the KoszulBrylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on KoszulBrylinski homology is nondegenerate. Finally, we compute the oszul-Brylinski homology for Poisson structures on ℂℙ1 × ℂℙ1.",

author = "Mathieu Sti{\'e}non",

year = "2011",

doi = "10.1093/imrn/rnq084",

language = "English (US)",

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pages = "553--571",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

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AU - Stiénon, Mathieu

PY - 2011

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AB - In this note, we study the KoszulBrylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on KoszulBrylinski homology is nondegenerate. Finally, we compute the oszul-Brylinski homology for Poisson structures on ℂℙ1 × ℂℙ1.

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U2 - 10.1093/imrn/rnq084

DO - 10.1093/imrn/rnq084

M3 - Article

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SP - 553

EP - 571

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 3

ER -

Holomorphic koszulBrylinski homology

Abstract

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