The Fano of lines, the Kuznetsov component, and a flop
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908421660344320 |
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| author | Kemboi, Kimoi Segal, Ed |
| author_facet | Kemboi, Kimoi Segal, Ed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Fano of lines, the Kuznetsov component, and a flop Kemboi, Kimoi Segal, Ed Algebraic Geometry 14F08 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. |
| title | The Fano of lines, the Kuznetsov component, and a flop |
| topic | Algebraic Geometry 14F08 |
| url | https://arxiv.org/abs/2506.20559 |