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Quadrics on Gushel-Mukai varieties

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arxiv 2409.03528 v1 pith:J7WMQAVX submitted 2024-09-05 math.AG

Olivier Debarre , Alexander Kuznetsov This is my paper · ORCID
classification math.AG
keywords dimensionquadricsgushel-mukaihilbertschemesvarietiesassociatedblowup
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abstract

We study Hilbert schemes of quadrics of dimension $k \in \{0,1,2,3\}$ on smooth Gushel-Mukai varieties $X$ of dimension $n \in \{2,3,4,5,6\}$ by relating them to the relative Hilbert schemes of linear subspaces of dimension $k + 1$ of a certain family, naturally associated with $X$, of quadrics of dimension $n - 1$ over the blowup of $\mathbf{P}^5$ at a point.

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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. 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.

  2. EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds

    math.AG 2025-12 conditional novelty 6.0 of 10

    For every strongly smooth ordinary Gushel–Mukai surface, the double dual EPW sextic is the Bridgeland moduli space of semistable objects with Mukai vector (1,0,−1), and analogous identifications hold for double EPW se...

  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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