RATIONALITY OF PESKINE VARIETIES

Vladimiro Benedetti (1) , Daniele Faenzi (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Algèbre et géométrie

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 hyperkähler fourfold associated to the Peskine sixfold.

Mots clés: rationality; hyperKahler

Domaines: Géométrie algébrique [math.AG]

Vladimiro Benedetti, Daniele Faenzi. RATIONALITY OF PESKINE VARIETIES. 2023. ⟨hal-03873604v2⟩