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arXiv · 2406.00463

Certaines fibrations en surfaces quadriques r\'eelles

Jean-Louis Colliot-Thélène·Alena Pirutka
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Abstract

We consider the question whether a real threefold X fibred into quadric surfaces over the real projective line is stably rational (over R) if the topological space X(R) is connected. We give a counterexample. When all geometric fibres are irreducible, the question is open. We investigate a family of such fibrations for which the intermediate jacobian technique is not available. We produce two independent methods which in many cases enable one to prove decomposition of the diagonal.

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Jean-Louis Colliot-Thélène, Alena Pirutka. 2024-06-01. Certaines fibrations en surfaces quadriques r\'eelles. https://arxiv.org/abs/2406.00463

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