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arXiv · 2506.20559

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

Kimoi Kemboi·Ed Segal
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Abstract

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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Kimoi Kemboi, Ed Segal. 2025-06-25. The Fano of lines, the Kuznetsov component, and a flop. https://arxiv.org/abs/2506.20559

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