Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections
- Autores: Vladimir Baranovsky, Viktor L. Ginzburg
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 2-3, 2010, págs. 211-230
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n2.a2
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Resumen
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 $\oo_X$ to a sheaf of noncommutative algebras and of the sheaves $\oo_Y$ and $\oo_Z$ to sheaves of right and left modules over the deformed algebra, respectively, gives rise to a Batalin-Vilkoviski algebra structure on the Tor-sheaf ${\scr{T}\!}or^{\oo_X}_\idot(\oo_Y,\oo_Z)$. 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 \cite{BF}, who studied intersections of Lagrangian submanifolds in a symplectic manifold.
