1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Description
Smooth quadric bundles over rational bases are frequently known to have rational deformation types and are often known to be unirational. On the other hand, for r>2, no smooth r-fold quadric bundle over a rational base has previously been known to be non-rational. In this talk we explain how to show that for any positive integer r, there is a wide class of smooth r-fold quadric bundles over rational bases which are not stably rational. In the proofs, we introduce a generalization of the specialization method of Voisin and Colliot-Thélène—Pirutka, which avoids explicit resolutions of singularities. This allows to apply the specialization method to many new situations which were not accessible before.
