The Fano of lines, the Kuznetsov component, and a flop
Algebraic Geometry
2025-06-26 v1
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.
Keywords
Cite
@article{arxiv.2506.20559,
title = {The Fano of lines, the Kuznetsov component, and a flop},
author = {Kimoi Kemboi and Ed Segal},
journal= {arXiv preprint arXiv:2506.20559},
year = {2025}
}
Comments
14 pages. Comments welcome