Formality of Koszul brackets and deformations of holomorphic Poisson manifolds
Formality of Koszul brackets and deformations of holomorphic Poisson manifolds
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DOI：
10.4310/hha.2012.v14.n2.a4
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发表时间：
2011-09
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影响因子：
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通讯作者：
D. Fiorenza;M. Manetti
中科院分区：
文献类型：
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作者：
D. Fiorenza;M. Manetti
我们证明，如果微分 Gerstenhaber 代数的生成元满足某些嘉当型恒等式，则相应的李括号是形式化的。几何示例包括泊松流形的平移 de Rham 复形以及在拉格朗日子流形上消失的辛流形上微分形式的子复形，并赋予 Koszul 括号。作为推论，我们概括了希钦关于全纯泊松流形变形的最新结果。
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.