On the Kähler structures over Quot schemes, II

Abstract

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\ge 2$, and let ${\mathcal{O}}_X$ denote the sheaf of holomorphic functions on $X$. Fix positive integers $r$ and $d$ and let $\mathcal{Q}(r,d)$ be the Quot scheme parametrizing all torsion coherent quotients of ${\mathcal{O}}_X^{\oplus r}$ of degree $d$. We prove that $\mathcal{Q}(r,d)$ does not admit a Kähler metric whose holomorphic bisectional curvatures are all nonnegative.

Illinois Journal of Mathematics (to appear)