Seminar

Let X be a holomorphic symplectic variety and F a coherent sheaf on X. Then a natural question to ask is if we take a deformation quantization of X can we also quantize the coherent sheaf F? We give an answer to this question, up to order 2, when the coherent sheaf is a direct image of a vector bundle supported on a smooth subvariety. If time permits we will also construct BV differentials on Tor and Ext groups between modules which admit quantizations. This is joint work with V.Baranovsky and V. Ginzburg.