Seminario Nacional de Geometría Algebraica en línea

Resumen:

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.