Papers › Symmetric locally free resolutions and rationality problems
Symmetric locally free resolutions and rationality problems
Gilberto Bini, Grzegorz Kapustka, Michał Kapustka
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We show that the birationality class of a quadric surface bundle over ℙ² is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over ℙ² 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.
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