L-equivalence and Fourier--Mukai partners of cubic fourfolds

Fuente: arXiv
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Autori principali: Meinsma, Reinder, Moschetti, Riccardo
Natura: Preprint
Pubblicazione: 2025
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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