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Twisted cubics on cubic fourfolds and stability conditions

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arxiv 1802.01134 v2 pith:F5JVWPTQ submitted 2018-02-04 math.AG

Chunyi Li , Laura Pertusi , Xiaolei Zhao This is my paper · ORCID
classification math.AG
keywords cubicfourfoldseightfoldfanofourfoldlehntheoremtorelli
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We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic curves in a cubic fourfold non containing a plane, as moduli spaces of Bridgeland stable objects in the Kuznetsov component. As a consequence, we reprove the categorical version of Torelli Theorem for cubic fourfolds, we obtain the identification of the period point of LLSvS eightfold with that of the Fano variety, and we discuss derived Torelli Theorem for cubic fourfolds.

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Cited by 2 Pith papers

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

  1. The hyper-Kummer construction

    math.AG 2026-07 accept novelty 8.0 of 10

    A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.

  2. 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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