Cyclic covers that are not stably rational

J. L. Colliot-Thélène, A. V. Pirutka

Research output: Contribution to journalArticle

Abstract

Using methods developed by Kollár, Voisin, ourselves and Totaro, we prove that a cyclic cover of PCn , n ≥ 3, of prime degree p, ramified along a very general hypersurface f(x0, ⋯ , xn) = 0 of degree mp, is not stably rational if m(p-1) ≤ n+1 6 mp. In dimension 3 we recover double covers of PC3 ramified along a very general surface of degree 4 (Voisin) and double covers of PC3 ramified along a very general surface of degree 6 (Beauville). We also find double covers of PC4 ramified along a very general hypersurface of degree 6. This method also enables us to produce examples over a number field.

Original languageEnglish (US)
Pages (from-to)665-677
Number of pages13
JournalIzvestiya Mathematics
Volume80
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Chow group of zero-cycles
  • Cyclic covers
  • Stable rationality

ASJC Scopus subject areas

  • Mathematics(all)

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