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arXiv · 1109.4309

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Domenico Fiorenza·Marco Manetti
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Abstract

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket. As a corollary we generalize a recent result by Hitchin on deformations of holomorphic Poisson manifolds.

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BibTeXRIS

Domenico Fiorenza, Marco Manetti. 2012-05-14. Formality of Koszul brackets and deformations of holomorphic Poisson manifolds. https://doi.org/10.4310/hha.2012.v14.n2.a4

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