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, 25(8), 1-35 [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 bundlesFile | Dimensione | Formato | |
---|---|---|---|
BKK_CCM.pdf
accesso aperto
Tipologia:
Pre-print
Dimensione
393.15 kB
Formato
Adobe PDF
|
393.15 kB | Adobe PDF | Visualizza/Apri |
bini_symmetric_resolution.pdf
Solo gestori archvio
Tipologia:
Versione Editoriale
Dimensione
537.31 kB
Formato
Adobe PDF
|
537.31 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.