Stable rationality of quadric and cubic surface bundle fourfolds

Asher Auel, Christian Böhning, Alena Pirutka

Research output: Contribution to journalArticlepeer-review

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)

Fingerprint Dive into the research topics of 'Stable rationality of quadric and cubic surface bundle fourfolds'. Together they form a unique fingerprint.

Cite this