Quot scheme and deformation quantization (Q6617372)

Given a compact connected Riemannian surface \(X\)\ and a projective structure \(P\)\ on \(X\)\ with \(\mathcal{Q}\left( r,d\right) \) denoting the quot scheme parametrization of all torsion quotients of \(\mathcal{O}_{X}^{\oplus r}\)\ of degree \(d\), this paper shows (Theorem 5.1) that \(\mathcal{U}\subset T^{\ast }\mathcal{Q}\)\ rigged with the holomorphic symplectic form \(\theta _{\mathcal{U}}\), where \(\mathcal{U}\subset T^{\ast}\mathcal{Q}\)\ is a certain Zariski subset, has a natrual deformation quantization. \textit{D. Ben-Zvi} and \textit{I. Biswas} [Lett. Math. Phys. 54, No. 1, 73--82 (2000; Zbl 0979.53094)] have already addressed the case when \(r=1=d\).