Quot scheme and deformation quantization

Abstract

Let $X$ be a compact connected Riemann surface, and let $\mathcal{Q}(r,d)$ denote the quot scheme parametrizing the torsion quotients of ${\mathcal{O}}_X^{\oplus r}$ of degree $d$. Given a projective structure $P$ on $X$, we show that the cotangent bundle $T^{\ast }\mathcal{U}$ of a certain nonempty Zariski open subset $\mathcal{U}\subset \mathcal{Q}(r,d)$, equipped with the natural Liouville symplectic form, admits a canonical deformation quantization. When $r=1=d$, then $\mathcal{Q}(r,d)=X$; this case was addressed earlier in \cite{BB}.

Final version