TY - JOUR

T1 - Conic bundle fourfolds with nontrivial unramified brauer group

AU - Auel, Asher

AU - Bohning, Christian

AU - Von Bothmer, H. C.G.

AU - Pirutka, Alena

N1 - Funding Information:
Received April 22, 2017, and, in revised form, April 4, 2019. partially supported by the NSA grant H98230-16-1-032.
Publisher Copyright:
© 2020 American Mathematical Society. All rights reserved.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1090/jag/743

DO - 10.1090/jag/743

M3 - Article

AN - SCOPUS:85090256815

VL - 29

SP - 285

EP - 327

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

SN - 1056-3911

IS - 2

ER -