Counting Fourier-Mukai partners of cubic fourfolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908561527799808 |
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| author | Böhning, Christian von Bothmer, Hans-Christian Graf Marquand, Lisa |
| author_facet | Böhning, Christian von Bothmer, Hans-Christian Graf Marquand, Lisa |
| contents | We develop an algorithm to count the number of virtual Fourier-Mukai partners for a given cubic fourfold, with initial input the primitive algebraic lattice and transcendental Hodge structure. Under some mild assumptions, we prove that our virtual count is enough to recover the actual count of Fourier-Mukai partners. We apply our algorithm to examples of cubics with a symplectic automorphism. In particular, we prove that a general cubic with a symplectic involution has 1120 non-trivial Fourier-Mukai partners, each admitting an Eckardt involution, and all birational. As a corollary, we prove that admitting a symplectic automorphism is not a Fourier-Mukai invariant for cubic fourfolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting Fourier-Mukai partners of cubic fourfolds Böhning, Christian von Bothmer, Hans-Christian Graf Marquand, Lisa Algebraic Geometry 14E05, 14J35, 14J70, 14F08 We develop an algorithm to count the number of virtual Fourier-Mukai partners for a given cubic fourfold, with initial input the primitive algebraic lattice and transcendental Hodge structure. Under some mild assumptions, we prove that our virtual count is enough to recover the actual count of Fourier-Mukai partners. We apply our algorithm to examples of cubics with a symplectic automorphism. In particular, we prove that a general cubic with a symplectic involution has 1120 non-trivial Fourier-Mukai partners, each admitting an Eckardt involution, and all birational. As a corollary, we prove that admitting a symplectic automorphism is not a Fourier-Mukai invariant for cubic fourfolds. |
| title | Counting Fourier-Mukai partners of cubic fourfolds |
| topic | Algebraic Geometry 14E05, 14J35, 14J70, 14F08 |
| url | https://arxiv.org/abs/2509.22491 |