EPW sextics vs EPW cubes
Algebraic Geometry
2024-02-05 v2
Abstract
We study a correspondence between double EPW cubes and double EPW sextics, two families of polarized hyper-K\"ahler manifolds related to Gushel--Mukai fourfolds. We infer relations between these families in terms of Hodge structures and moduli spaces of elliptic curves. As an application, we prove that a very general double EPW cube is the moduli space of stable objects with respect to a suitable stability condition on the Kuznetsov component of its corresponding Gushel--Mukai fourfolds; this answers a problem posed by Perry, Pertusi and Zhao.
Keywords
Cite
@article{arxiv.2202.00301,
title = {EPW sextics vs EPW cubes},
author = {Grzegorz Kapustka and Michal Kapustka and Giovanni Mongardi},
journal= {arXiv preprint arXiv:2202.00301},
year = {2024}
}