We show that the birationality class of a quadric surface bundle over ℙ2ℙ2 is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over ℙ2ℙ2 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

Gilberto Bini, G.K. (2022). Symmetric locally free resolutions and rationality problems. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 1-28 [10.1142/S021919972250033X].

Symmetric locally free resolutions and rationality problems

Gilberto Bini;
2022-07-11

Abstract

We show that the birationality class of a quadric surface bundle over ℙ2ℙ2 is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over ℙ2ℙ2 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
Settore MAT/03 - Geometria
https://www.worldscientific.com/doi/pdf/10.1142/S021919972250033X?download=true
Gilberto Bini, G.K. (2022). Symmetric locally free resolutions and rationality problems. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 1-28 [10.1142/S021919972250033X].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/566663
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