Let $X$ be a smooth projective surface over an algebraically closed field $k$ such that $char(k) \neq 2$. 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 $\ell \neq 2$, 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 $d \geq 3$. 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 $Q(r,d) \rightarrow X^{ [d]}$ induces an isomorphism on cohomological Brauer groups.
Categories: math.AG