Mathematics Seminar Date: Thursday, 31 August 2023 Time: 2:00 PM Venue: Lecture Hall 06 Brauer group of Hilbert Scheme of two points of a smooth projective surface and applications Yashonidhi Pandey IISER Mohali. 310823 Abstract Let $X$ be a smooth projective surface over an algebraically closed field $k$ such that $p=char(k) \neq 2$. For $d \geq 2$, let $X^{[d]}$ denote the punctual Hilbert scheme of zerodimensional quotients of degree $d$ and $X^{(d)}$ denote the symmetric product of $X$. For $\ell \neq \{2, p \}$, we give a formula for the $\ell$primary part of the Brauer group of $X^{[2]}$. We show that the Hilbert to Chow morphism $\omega_2: X^{[2]} \rightarrow X^{(2)}$ induces an isomorphism of cohomological Brauer groups for $d=2$ and a similar partial result for $d \geq 3$.
