Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Hilbert squares of genus $16$ $K3$ surfaces
Speaker: Arnab Roy, TIFR, Mumbai
Date: November 18, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: Polarized Hilbert schemes of points on $K3$ surfaces form a fundamental class of polarized hyper-Kahler manifolds, while moduli spaces of sheaves of fixed mukai vector on $K3$ surfaces have produced non trivial examples of hyper-Kahler manifolds. Following the preprint {\tt arXiv:2510.26488v1} by Junyu Meng, in this talk we will see that for a general polarized $K3$ surface $(S,h)$ and its Fourier-Mukai partner $(S',h')$, the second hilbert power of $S$ is isomorphic to moduli space of stable sheaves on $S'$ with Mukai vector $(2,h',7)$. Time permitting we will discuss the connection of this result with the Debarre-Voisin construction of hyper-Kahler manifolds.