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Stable Rationality of Cyclic Covers of Projective Spaces

Part of: Arithmetic problems. Diophantine geometry Cycles and subschemes Birational geometry

Published online by Cambridge University Press:  11 January 2019

Takuzo Okada
Takuzo Okada*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan (okada@cc.saga-u.ac.jp)
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Abstract

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.

Keywords

stable rationalitycyclic cover

MSC classification

Primary: 14E08: Rationality questions
Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14G17: Positive characteristic ground fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 667 - 682
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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