L-equivalence and 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_ | 1866910019629350912 |
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| author | Meinsma, Reinder Moschetti, Riccardo |
| author_facet | Meinsma, Reinder Moschetti, Riccardo |
| contents | We study L-equivalence in the Grothendieck ring of varieties and its interaction with categorical invariants of cubic fourfolds. Assuming a Derived Torelli-type criterion for Kuznetsov components and a mild condition on the discriminant of the transcendental lattice, we prove a counting formula for Fourier--Mukai partners of such cubic fourfolds. As an application, we exhibit cubic fourfolds with a fixed algebraic lattice admitting a unique non-trivial Fourier--Mukai partner, which is trivially L-equivalent to the original. Finally, we show that L-equivalence classes of cubic fourfolds are finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L-equivalence and Fourier--Mukai partners of cubic fourfolds Meinsma, Reinder Moschetti, Riccardo Algebraic Geometry We study L-equivalence in the Grothendieck ring of varieties and its interaction with categorical invariants of cubic fourfolds. Assuming a Derived Torelli-type criterion for Kuznetsov components and a mild condition on the discriminant of the transcendental lattice, we prove a counting formula for Fourier--Mukai partners of such cubic fourfolds. As an application, we exhibit cubic fourfolds with a fixed algebraic lattice admitting a unique non-trivial Fourier--Mukai partner, which is trivially L-equivalent to the original. Finally, we show that L-equivalence classes of cubic fourfolds are finite. |
| title | L-equivalence and Fourier--Mukai partners of cubic fourfolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.08651 |