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EPW sextics vs EPW cubes

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arxiv 2202.00301 v2 pith:U23KK6ZK submitted 2022-02-01 math.AG

Grzegorz Kapustka , Michal Kapustka , Giovanni Mongardi This is my paper · ORCID
classification math.AG
keywords doublecubesfamiliesfourfoldsgushel--mukaimodulisexticsahler
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The finite degree formula for normalized volumes

    math.AG 2026-07 accept novelty 8.0 of 10

    For finite crepant morphisms of klt singularities, normalized volume scales exactly by the degree of the morphism.

  2. Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds

    math.AG 2025-01 accept novelty 7.0 of 10

    The double EPW cube of a general Gushel-Mukai fourfold is the MRC quotient of the Hilbert scheme of twisted cubics, and it admits a Lagrangian covering family.

  3. On two families of Enriques categories over K3 surfaces

    math.AG 2024-12 unverdicted novelty 6.0 of 10

    The moduli spaces in two families of Enriques categories recover Beauville's involution, the double EPW sextic and cube, and a new birational involution on O'Grady's tenfold.

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