Generic strange duality for $K3$ surfaces

Abstract

Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier-Mukai techniques. Applications to Brill-Noether theory for sheaves on $K3$s are also obtained. The appendix written by Kota Yoshioka discusses the behavior of the moduli spaces under change of polarization, as needed in the argument.

Appendix is written by Kota Yoshioka

References in corpus (2)

• On the Cobordism Class of the Hilbert Scheme of a Surface
• Irreducibility of moduli spaces of vector bundles on K3 surfaces

Cited by in corpus (10)

• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Generating functions for K-theoretic Donaldson invariants and Le Potier's strange duality
• On the strange duality conjecture for abelian surfaces II
• Fourier-Mukai transforms and stable sheaves on Weierstrass elliptic surfaces
• Rank-one sheaves and stable pairs on surfaces
• The cohomology of the general stable sheaf on a K3 surface
• Moduli spaces of stable sheaves over quasi-polarized surfaces, and the relative Strange Duality morphism
• Representations in Strange Duality: Hilbert Schemes paired with higher rank spaces
• Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on ${\mathbb{P}}^2$