Symmetric locally free resolutions and rationality problems

Abstract

We show that the birationality class of a quadric surface bundle over ${\mathbb{P}}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over ${\mathbb{P}}^2$ with discriminant curves of fixed degree. In particular, we construct explicit models of these bundles for some discriminant data. Among others, we obtain various birational models of a nodal Gushel-Mukai fourfold, as well as of a cubic fourfold containing a plane. Finally, we prove stable irrationality of several types of quadric surface bundles.

27 pages, to appear in Communications in Contemporary Mathematics

References in corpus (3)

• On the rationality problem for quadric bundles
• Quadric surface bundles over surfaces and stable rationality
• Degenerations of Gushel-Mukai fourfolds, with a view towards irrationality proofs

Cited by in corpus (1)

• Quadric bundles and hyperbolic equivalence