6533b853fe1ef96bd12ac0ea
RESEARCH PRODUCT
Symmetric locally free resolutions and rationality problems
Gilberto BiniGrzegorz KapustkaMichał Kapustkasubject
Mathematics - Algebraic GeometryMathematics::Algebraic GeometryApplied MathematicsGeneral MathematicsFOS: Mathematics13D02 14E08 14D06 14J32 14J45quadric bundle Brauer class symmetric resolutions rationalitySettore MAT/03 - GeometriaMathematics - Commutative AlgebraCommutative Algebra (math.AC)Mathematics::Symplectic GeometryAlgebraic Geometry (math.AG)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-07-11 | Communications in Contemporary Mathematics |