Rationality of peskine varieties

Vladimiro Benedetti; Daniele Faenzi

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arXiv · 2211.16129

Rationality of peskine varieties

Vladimiro Benedetti·Daniele Faenzi

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Abstract

We study the rationality of the Peskine sixfolds in P^9. We prove the rationality of the Peskine sixfolds in the divisor D^{3,3,10} inside the moduli space of Peskine sixfolds and we provide a cohomological condition which ensures the rationality of the Peskine sixfolds in the divisor D^{1,6,10} (notation from [BS]). We conjecture, as in the case of cubic fourfolds containing a plane, that the cohomological condition translates into a cohomological and geometric condition involving the Debarre-Voisin hyperk{\"a}hler fourfold associated to the Peskine sixfold.

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Vladimiro Benedetti, Daniele Faenzi. 2022-11-29. Rationality of peskine varieties. https://arxiv.org/abs/2211.16129

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