Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections
Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections
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各向同性交点上的 Gerstenhaber-Batalin-Vilkoviski 结构
DOI：
10.4310/mrl.2010.v17.n2.a2
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
V. Ginzburg
中科院分区：
文献类型：
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作者：
V. Baranovsky;V. Ginzburg
设Y，Z是光滑代数Poisson簇X中的一对光滑余迷向子簇。本文证明了：结构层O_X到非交换代数层以及层O_Y和O_Z到变形代数上的右模层和左模层的一阶变形的任何数据，都会在Tor-sheaf Tor^{O_X}_*（O_Y，O_Z）上产生Batalin-Vilkoviski代数结构.托尔层上的诱导格斯坦哈伯括号原来是正则定义的;它是独立的选择所涉及的变形。对于Ext-sheaves也有类似的结果。
我们的建设是出于动机，并密切相关的，结果Bewald-Fantechi，谁考虑的情况下，拉格朗日子流形的辛流形。
Let Y,Z be a pair of smooth coisotropic subvarieties in a smooth algebraic Poisson variety X. We show that any data of first order deformation of the structure sheaf O_X to a sheaf of noncommutative algebras and of the sheaves O_Y and O_Z to sheaves of right and left modules over the deformed algebra, respectively, gives rise to a Batalin-Vilkoviski algebra structure on the Tor-sheaf Tor^{O_X}_*(O_Y, O_Z). The induced Gerstenhaber bracket on the Tor-sheaf turns out to be canonically defined; it is independent of the choices of deformations involved. There are similar results for Ext-sheaves as well.
Our construction is motivated by, and is closely related to, a result of Behrend-Fantechi, who considered the case of Lagrangian submanifolds in a symplectic manifold.