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Variétés rationnelles

Horaires : Le vendredi 20 octobre 2017, 17h - 18h

Lieu : ENS, salle W

The rationality problem for quadric bundles

S. Schreieder (Bonn)

We study the rationality problem for quadric bundles X over rational bases S. By a theorem of Lang, such bundles are rational if r > 2^n-2, where r denotes the fibre dimension and n = dim(S) denotes the dimension of the base. We show that this result is sharp. In fact, for any r at most 2^n-2, we show that many smooth r-fold quadric bundles over rational n-folds are not even stably rational. Our result is based on a generalization of the specialization method of Voisin and Colliot-Thélène-Pirutka.

 

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