Stability and certain ${\mathbb{P}}^n$-functors

Abstract

Let $X$ be a K3 surface. We prove that Addington's ${\mathbb{P}}^n$-functor between the derived categories of $X$ and the Hilbert scheme of points $X^{[k]}$ maps stable vector bundles on $X$ to stable vector bundles on $X^{[k]}$, given some numerical conditions are satisfied.

8 pages. Comments welcome! v2: shorter title, slight improvements after referee report. Final version

References in corpus (3)

• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• Stable vector bundles on generalized Kummer varieties
• Stability of some vector bundles on Hilbert schemes of points on K3 surfaces