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 $CH_0$-trivial resolutions of singularities.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2017
- DOI:
- 10.48550/arXiv.1706.01356
- arXiv:
- arXiv:1706.01356
- Bibcode:
- 2017arXiv170601356S
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14E08;
- 14M20;
- 14D06
- E-Print:
- 31 pages