On the double EPW sextic associated to a Gushel-Mukai fourfold

Abstract

In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover ${\tilde{Y}}_A$ of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold is birationally equivalent to a moduli space of (twisted) stable sheaves on a K3 surface. In particular, we prove that ${\tilde{Y}}_A$ is birational to the Hilbert scheme of two points on a K3 surface if and only if the Gushel-Mukai fourfold is Hodge-special with discriminant $d$ such that the negative Pell equation ${\mathcal{P}}_{d/2}(-1)$ is solvable in $\mathbb{Z}$.

29 pages

References in corpus (1)

• Stability conditions on Kuznetsov components

Cited by in corpus (1)

• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties