Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational

TL;DR

This paper establishes a criterion to determine when Hilbert schemes of points on K3 surfaces are birational, leading to many examples of non-birational yet derived equivalent schemes, enriching the understanding of their geometric relationships.

Contribution

It introduces a new criterion for birationality of Hilbert schemes on K3 surfaces, enabling the construction of numerous non-birational derived equivalent examples.

Findings

Identified conditions for birationality of Hilbert schemes on K3 surfaces

Generated many examples of non-birational derived equivalent schemes

Enhanced understanding of the relationship between birationality and derived equivalence

Abstract

We provide a criterion for when Hilbert schemes of points on K3 surfaces are birational. In particular, this allows us to generate a plethora of examples of non-birational Hilbert schemes which are derived equivalent.