Ulrich Sheaves on the Hilbert Square of K3 and Abelian Surfaces

Abstract

We prove the existence of Ulrich sheaves on the Hilbert scheme of two points on a polarized K3 surface or an abelian surface. The construction proceeds by descending Ulrich bundles on the surface to the symmetric square and lifting them to the Hilbert square via the crepant Hilbert--Chow resolution. Finally, we estimate a bound for Ulrich complexity of the Hilbert Square.