Stable rationality of cyclic covers of projective spaces

Abstract

The main aim of this paper is to show that a cyclic cover of ${\mathbb{P}}^n$ branched along a very general divisor of degree $d$ is not stably rational provided that $n\ge 3$ and $d\ge n+1$. 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.

13 pages

References in corpus (5)

• Four-dimensional projective orbifold hypersurfaces
• On stable rationality of Fano threefolds and del Pezzo fibrations
• Torsion orders of complete intersections
• A very general sextic double solid is not stably rational
• Revêtements cycliques qui ne sont pas stablement rationnels

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• Quadric surface bundles over surfaces and stable rationality
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• Stable rationality of quadric and cubic surface bundle fourfolds
• A very general quartic double fourfold is not stably rational
• Stable rationality of del Pezzo fibrations of low degree over projective spaces
• Torsion orders of Fano hypersurfaces
• Stable rationality of orbifold Fano threefold hypersurfaces
• Rationality, universal generation and the integral Hodge conjecture
• Intersections of three quadrics in ${\mathbb{P}}^7$
• Stable rationality of index one Fano hypersurfaces containing a linear space
• Smooth weighted hypersurfaces that are not stably rational