Conic bundle fourfolds with nontrivial unramified brauer group

Asher Auel, Christian Bohning, H. C.G. Von Bothmer, Alena Pirutka

Research output: Contribution to journalArticlepeer-review

Abstract

We derive a formula for the unramified Brauer group of a general class of rationally connected fourfolds birational to conic bundles over smooth threefolds. We produce new examples of conic bundles over P3 where this formula applies and which have nontrivial unramified Brauer group. The construction uses the theory of contact surfaces and, at least implicitly, matrix factorizations and symmetric arithmetic Cohen-Macaulay sheaves, as well as the geometry of special arrangements of rational curves in P2. We also prove the existence of universally CH0-trivial resolutions for the general class of conic bundle fourfolds we consider. Using the degeneration method, we thus produce new families of rationally connected fourfolds whose very general member is not stably rational.

Original languageEnglish (US)
Pages (from-to)285-327
Number of pages43
JournalJournal of Algebraic Geometry
Volume29
Issue number2
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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