Double covers of smooth quadric threefolds with Artin–Mumford obstructions to rationality

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-11-19 DOI:10.1112/jlms.70028

Alexandra Kuznetsova

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引用次数: 0

Abstract

We study obstructions to rationality on a nodal Fano threefold $M$ that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in $P^{4}$ . We prove that if $M$ admits an Artin–Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin–Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new.

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具有阿尔廷-芒福德合理性障碍的光滑四元三次方的双盖

我们研究了节点法诺三折 M $M$的合理性障碍，它是光滑四元三折的双盖，与 P 4 $\mathbb {P}^4$ 中的四元三折相交。我们证明，如果 M $M$ 存在阿尔丁-芒福德理性障碍，那么它就属于三个明确描述的族之一。反之，这些族中任何一个族的一般元素都存在阿廷-芒福德理性障碍。这三个系中只有一个系是已知的，其他两个具有合理性障碍的节点法诺三折叠系都是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.