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arXiv · 1611.06687

Fourier-Mukai partners for very general special cubic fourfolds

Laura Pertusi
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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 $d \equiv 2 (\text{mod}\,6)$; else, if $d \equiv 0 (\text{mod}\,6)$, the cubic fourfold has $\lceil m/2 \rceil$ Fourier-Mukai partners.

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Laura Pertusi. 2016-11-21. Fourier-Mukai partners for very general special cubic fourfolds. https://arxiv.org/abs/1611.06687

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