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Conic bundle fourfolds with nontrivial unramified Brauer group
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Auel, Asher, Böhning, Christian, Graf von Bothmer, Hans-Christian and Pirutka, Alena (2020) Conic bundle fourfolds with nontrivial unramified Brauer group. Journal of Algebraic Geometry, 29 . pp. 285-327. doi:10.1090/jag/743 ISSN 1056-3911.
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Official URL: https://doi.org/10.1090/jag/743
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Algebraic varieties, Sheaf theory | ||||||||
Journal or Publication Title: | Journal of Algebraic Geometry | ||||||||
Publisher: | University Press, Inc. | ||||||||
ISSN: | 1056-3911 | ||||||||
Official Date: | April 2020 | ||||||||
Dates: |
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Volume: | 29 | ||||||||
Page Range: | pp. 285-327 | ||||||||
DOI: | 10.1090/jag/743 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | “First published in Journal of Algebraic Geometry in [volume/issue number and year], published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | © Copyright 2019 American Mathematical Society | ||||||||
Date of first compliant deposit: | 6 June 2019 | ||||||||
Date of first compliant Open Access: | 10 June 2019 | ||||||||
RIOXX Funder/Project Grant: |
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