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Izvestiya: Mathematics, 2016, Volume 80, Issue 4, Pages 665–677
DOI: https://doi.org/10.1070/IM8429
(Mi im8429)
 

This article is cited in 27 scientific papers (total in 27 papers)

Cyclic covers that are not stably rational

J.-L. Colliot-Thélèneab, A. Pirutkac

a Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
b Université de Paris-Sud Mathematiques, Département de Mathématique
c Ècole Polytechnique CNRS, Centre de Mathématiques Appliquées
References:
Abstract: Using methods developed by Kollár, Voisin, ourselves and Totaro, we prove that a cyclic cover of $\mathbb P_{\mathbb C}^n$, $n\geqslant 3$, of prime degree $p$, ramified along a very general hypersurface $f(x_0,\dots , x_n)=0$ of degree $mp$, is not stably rational if $m(p-1) <n+1\leqslant mp$. In dimension 3 we recover double covers of $\mathbb P^3_{\mathbb C}$ ramified along a very general surface of degree 4 (Voisin) and double covers of $\mathbb P^3_{\mathbb C}$ ramified along a very general surface of degree 6 (Beauville). We also find double covers of $\mathbb P^4_{\mathbb C}$ ramified along a very general hypersurface of degree 6. This method also enables us to produce examples over a number field.
Keywords: stable rationality, Chow group of zero-cycles, cyclic covers.
Received: 06.07.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 4, Pages 35–48
DOI: https://doi.org/10.4213/im8429
Bibliographic databases:
Document Type: Article
UDC: 512.752
Language: English
Original paper language: Russian
Citation: J.-L. Colliot-Thélène, A. Pirutka, “Cyclic covers that are not stably rational”, Izv. RAN. Ser. Mat., 80:4 (2016), 35–48; Izv. Math., 80:4 (2016), 665–677
Citation in format AMSBIB
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\paper Cyclic covers that are not stably rational
\jour Izv. RAN. Ser. Mat.
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  • https://doi.org/10.1070/IM8429
  • https://www.mathnet.ru/eng/im/v80/i4/p35
  • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:423
    Russian version PDF:56
    English version PDF:30
    References:58
    First page:17
     
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