Stable rationality of quadric and cubic surface bundle fourfolds

Asher Auel, Christian Böhning, Alena Pirutka

Research output: Contribution to journalArticle

Abstract

We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the specialization method for the Chow group of 0-cycles. Our main result is that a very general hypersurface X of bidegree (2, 3) in [InlineEquation not available: see fulltext.] is not stably rational. Via projections onto the two factors, [InlineEquation not available: see fulltext.] is a cubic surface bundle and [InlineEquation not available: see fulltext.] is a conic bundle, and we analyze the stable rationality problem from both these points of view. Also, we introduce, for any n⩾ 4 , new quadric surface bundle fourfolds [InlineEquation not available: see fulltext.] with discriminant curve [InlineEquation not available: see fulltext.] of degree 2n, such that Xn has nontrivial unramified Brauer group and admits a universally CH 0-trivial resolution.

Original languageEnglish (US)
Pages (from-to)732-760
Number of pages29
JournalEuropean Journal of Mathematics
Volume4
Issue number3
DOIs
StatePublished - Sep 1 2018

Keywords

  • Brauer group
  • Cubic surface bundles
  • Fano fourfolds
  • Quadric bundles
  • Stable rationality

ASJC Scopus subject areas

  • Mathematics(all)

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