On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors

TL;DR

This paper proves that the strange duality isomorphism for K3 surfaces extends over certain divisors in the moduli space, providing a global sheaf-theoretic interpretation and construction.

Contribution

It extends the known strange duality results for K3 surfaces to entire Noether-Lefschetz divisors, offering a global sheaf-theoretic framework.

Findings

Strange duality holds over Noether-Lefschetz divisors in the moduli space.

Provides a global sheaf isomorphism over these divisors.

Describes a global construction over the polarized K3 moduli space.

Abstract

We extend results on generic strange duality for K3 surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized K3s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized K3s.