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The Fano of lines, the Kuznetsov component, and a flop

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arxiv 2506.20559 v1 pith:MWTLRK7T submitted 2025-06-25 math.AG

The Fano of lines, the Kuznetsov component, and a flop

classification math.AG
keywords categoryderivedfourfoldcomponentcubicfanoflophyperkaehler
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The Kuznetsov component of the derived category of a cubic fourfold is a `non-commutative K3 surface'. Its symmetric square is hence a `non-commutative hyperkaehler fourfold'. We prove that this category is equivalent to the derived category of an actual hyperkaehler fourfold: the Fano of lines in the cubic. This verifies a conjecture of Galkin. One of the key steps in our proof is a new derived equivalence for a specific 12-dimensional flop.

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  1. Kuznetsov components and transcendental motives of cubic fourfolds

    math.AG 2026-06 unverdicted novelty 4.0

    For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.