Holomorphic koszulBrylinski homology

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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 languageEnglish (US)
Pages (from-to)553-571
Number of pages19
JournalInternational Mathematics Research Notices
Volume2011
Issue number3
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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