On the rationality problem for quadric bundles

Abstract

We classify all positive integers n and r such that (stably) non-rational complex r-fold quadric bundles over rational n-folds exist. We show in particular that for any n and r, a wide class of smooth r-fold quadric bundles over projective n-space are not stably rational if r lies in the interval from $2^{n-1}-1$ to $2^n-2$. In our proofs we introduce a generalization of the specialization method of Voisin and Colliot-Thélène--Pirutka which avoids universally $C{H}_0$-trivial resolutions of singularities.

31 pages; final version; to appear in Duke Math. Journal

References in corpus (1)

• Quadric surface bundles over surfaces and stable rationality

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