Derived-natural automorphisms on Hilbert schemes of points on generic K3 surfaces

TL;DR

This paper explores how derived category autoequivalences induce automorphisms on Hilbert schemes of points on generic K3 surfaces, providing a new perspective on their birational and biregular automorphisms.

Contribution

It characterizes birational and biregular involutions of Hilbert schemes of points on generic K3 surfaces via derived category autoequivalences.

Findings

Characterization of involutions induced by derived autoequivalences

Insight into automorphisms of Hilbert schemes on generic K3 surfaces

Connection between derived categories and geometric automorphisms

Abstract

The article revisits birational and biregular automorphisms of the Hilbert scheme of points on a K3 surface from the perspective of derived categories. Under the assumption that the K3 surface is generic, the birational and biregular involutions induced by autoequivalences on the derived category of the underlying K3 surface are characterized.