Brauer group of punctual Quot scheme of points on a smooth projective surface

Abstract

Let $X$ be a smooth projective surface over an algebraically closed field $k$ such that $char(k)\ne 2$. Let $X^{[d]}$ denote the punctual Hilbert scheme of zero dimensional quotients of degree $d$ and $X^{(d)}$ denote the symmetric product of $X$. For $\ell \ne 2$, we give a formula for the $\ell$-primary part of the Brauer group of $X^{[2]}$. We show that the Hilbert to Chow morphism induces an isomorphism of cohomological Brauer groups for $d=2$ and a similar result for $d\ge 3$. Let $Q(r,d)$ denote the punctual Quot-scheme parametrising zero dimensional quotients of ${\mathcal{O}}_X^{\oplus r}$ of degree $d$. We show that the natural morphism from $Q(r,d)\to X^{[d]}$ induces an isomorphism on cohomological Brauer groups.

References in corpus (1)

• A simply connected surface of general type with p_g=0 and K^2=2