Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

Abstract

Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $\mathcal{E}$ on $X\times M$ can be understood as a complete flat family of stable vector bundles on $M$ parametrized by $X$, which identifies $X$ with a smooth connected component of some moduli space of stable sheaves on $M$.

21 pages. Major revision after referee report. Improved the presentation and highlighted the use of the spherical twist and its inverse. Comments welcome!

References in corpus (2)

• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points

Cited by in corpus (2)

• Stable vector bundles on generalized Kummer varieties
• Stability and certain ${\mathbb{P}}^n$-functors