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arXiv · 2104.00810

Chern classes of quantizable coisotropic bundles

Vladimir Baranovsky
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Abstract

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of codimension $q$ and a vector bundle $E$ on $Y$. We show that if $j_* E$ admits a deformation quantization (as a module) then its characteristic class $\widehat{A}(M) exp(-c(\mathcal{O}_h)) ch(j_* E)$ lifts to a cohomology group associated to the null foliation of $Y$. Moreover, it can only be nonzero in degrees $2q, \ldots, 2(p+q)$. For Lagrangian $Y$ this reduces to a single degree $2q$. Similar results hold in the holomorphic category. This is a companion paper of a joint work with Victor Ginzburg on general quantizable sheaves.

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Vladimir Baranovsky. 2021-04-01. Chern classes of quantizable coisotropic bundles. https://arxiv.org/abs/2104.00810

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