The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2017-10-12 DOI:10.1090/JAG/724

B. Totaro

引用次数: 32

Abstract

We show that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0 p>0 . Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.

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法诺变种的Kodaira消失的失败，以及不是Cohen Macaulay的终端奇点

我们证明了Kodaira消失定理在任意特征p>0的光滑Fano变量上失效。在这些变种中，我们首先给出非科恩-麦考利端点奇点的第一个例子。通过另一种方法，我们在特征2上构造了一个3维(最低可能)的终端奇点，它不是Cohen-Macaulay。

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 Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.