Quot scheme and deformation quantization

Let X be a compact connected Riemann surface, and let Q ( r , d ) denote the quot scheme parametrizing the torsion quotients of O X ⊕ r of degree d . Given a projective structure P on X , we show that the cotangent bundle T ∗ U of a certain nonempty Zariski open subset U ⊂ Q ( r , d ) , equipped with the natural Liouville symplectic form, admits a canonical deformation quantization. When r = 1 = d , then Q ( r , d ) = X ; this case was addressed earlier in Ben-Zvi and Biswas ( Lett. Math. Phys. 54 (2000) 73–82).