Fourier-Mukai partners for very general special cubic fourfolds

DOI10.4310/MRL.2021.V28.N1.A9arXiv1611.06687MaRDI QIDQ6279960

Laura Pertusi

Publication date: 21 November 2016

Abstract: We exhibit explicit examples of very general special cubic fourfolds with discriminant $d$ admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting, we show that the number of Fourier-Mukai partners for a very general special cubic fourfold with discriminant $d$ and having an associated K3 surface, is equal to the number $m$ of Fourier-Mukai partners of its associated K3 surface, if $dequiv2(extmod,6)$; else, if $dequiv0(extmod,6)$, the cubic fourfold has $lceilm/2ceil$ Fourier-Mukai partners.

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) (4)-folds (14J35) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

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