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

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arxiv 1912.06935 v2 pith:F7FYY3O3 submitted 2019-12-14 math.AG

Alexander Perry , Laura Pertusi , Xiaolei Zhao This is my paper · ORCID
classification math.AG
keywords gushel-mukaikuznetsovvarietiesbridgelandcomponentsconditionseven-dimensionalmoduli
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We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case. As applications, we construct a new infinite series of unirational locally complete families of polarized hyperk\"{a}hler varieties of K3 type, and characterize Hodge-theoretically when the Kuznetsov component of an even-dimensional Gushel-Mukai variety is equivalent to the derived category of a K3 surface.

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  1. Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

    math.AG 2019-08 conditional novelty 6.0 of 10

    For general quartic double solids, two varieties are isomorphic if and only if their Kuznetsov components are equivalent, without assuming the equivalence has Fourier-Mumford type.

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