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1 February 2019 On the rationality problem for quadric bundles
Stefan Schreieder
Duke Math. J. 168(2): 187-223 (1 February 2019). DOI: 10.1215/00127094-2018-0041

Abstract

We classify all positive integers n and r such that (stably) nonrational 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 PCn are not stably rational if r[2n11,2n2]. In our proofs we introduce a generalization of the specialization method of Voisin and of Colliot-Thélène and Pirutka which avoids universally CH0-trivial resolutions of singularities.

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Stefan Schreieder. "On the rationality problem for quadric bundles." Duke Math. J. 168 (2) 187 - 223, 1 February 2019. https://doi.org/10.1215/00127094-2018-0041

Information

Received: 19 October 2017; Revised: 12 July 2018; Published: 1 February 2019
First available in Project Euclid: 8 November 2018

zbMATH: 07036862
MathSciNet: MR3909896
Digital Object Identifier: 10.1215/00127094-2018-0041

Subjects:
Primary: 14E08
Secondary: 14D06, 14J35, 14M20

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 2 • 1 February 2019
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