Geometry Seminar

University of Tor Vergata, Department of Mathematics

15th of November 2022, 14:30-15:30, room “Dal Passo”

Speaker

Alex Massarenti

(Università di Ferrara)

Title

On the unirationality of quadric bundles

Abstract

An variety X over a field is unirational if there is a dominant rational map from a projective space to X.

We will prove that a general quadric bundle, over a number field, with anti-canonical divisor of positive volume and discriminant of odd degree is unirational,

and that the same holds for quadric bundles over an arbitrary infinite field provided that they have a point and that their dimension is at most five.

As a consequence we will get the unirationality of any smooth 4-fold quadric bundle over the projective plane, over an algebraically closed field, and with discriminant of degree at most 12.