Friday, May 27, 2022 12:00 PM
Soheyla Feyzbakhsh (Imperial College London)

Consider the moduli space \$M_C(r; K_C)\$ of stable rank r vector bundles on a curve \$C\$ with canonical determinant, and let \$h\$ be the maximum number of linearly independent global sections of these bundles. If \$C\$ embeds in a K3 surface \$X\$ as a generator of \$Pic(X)\$ and the genus of \$C\$ is sufficiently high, I will show the Brill-Noether locus \$BN_C \subset M_C(r; K_C)\$ of bundles with \$h\$ global sections is a smooth projective Hyperkahler manifold, isomorphic to a moduli space of stable vector bundles on \$X\$. The main technique is to apply wall-crossing with respect to Bridgeland stability conditions on K3 surfaces.

The synchronous discussion for Soheyla Feyzbakhsh’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2022-05-27-sf (and will be deleted after ~3-7 days).