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 d equivalent to 2(mod 6); else, if d equivalent to 0(mod 6), the cubic fourfold has inverted right perpendicularm/2inverted left perpendicular Fourier-Mukai partners.

Fourier-Mukai partners for very general special cubic fourfolds / L. Pertusi. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 28:1(2021 Apr 19), pp. 213-243. [10.4310/MRL.2021.V28.N1.A9]

Fourier-Mukai partners for very general special cubic fourfolds

L. Pertusi
2021

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 d equivalent to 2(mod 6); else, if d equivalent to 0(mod 6), the cubic fourfold has inverted right perpendicularm/2inverted left perpendicular Fourier-Mukai partners.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/870875
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