Alexander Kuznetsov
Title: Quadric bundles and hyperbolic equivalence
Abstract:
A quadric bundle is a flat morphism Q \to X with fibers isomorphic to quadric hypersurfaces.
We discuss the operations of hyperbolic reduction and extension for quadric bundles and check
that they do not change the main invariants of Q such as the discriminant divisor and the Brauer
data. We show, moreover, that these operations can be used to transform any quadric bundle over
a projective plane to a quadric bundle contained in the projectivization of a direct sum of line
bundles. Similarly, any quadric bundle over a higher-dimensional projective space can be transform
to a quadric bundle contained in the projectivization of a vector bundle that enjoys some cohomology
vanishing.