Rationality of peskine varieties

2022/11/29 by Benedetti, Vladimiro, Faenzi, Daniele · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.16129

Abstract

We study the rationality of the Peskine sixfolds in P⁹. 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.

Cited by

• Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds

Related

• Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds
• Explicit rationality of some cubic fourfolds
• Rational fibered cubic fourfolds
• On rationality of nonsingular threefolds with a pencil of Del Pezzo surfaces of degree 4
• Divisors in the moduli space of Debarre-Voisin varieties