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stable rationality

Proceedings of the Edinburgh Mathematical Society (1)

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Stable Rationality of Cyclic Covers of Projective Spaces
Part of
Takuzo Okada
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019

Published online by Cambridge University Press:

11 January 2019, pp. 667-682
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The main aim of this paper is to show that a cyclic cover of ℙn branched along a very general divisor of degree d is not stably rational, provided that n ≥ 3 and d ≥ n + 1. This generalizes the result of Colliot-Thélène and Pirutka. Generalizations for cyclic covers over complete intersections and applications to suitable Fano manifolds are also discussed.