The behavior of essential dimension under specialization, II

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-10-03 DOI:10.2140/ant.2023.17.1925

Zinovy Reichstein, Federico Scavia

引用次数: 2

Abstract

Let $G$ be a linear algebraic group over a field. We show that, under mild assumptions, in a family of primitive generically free $G$ -varieties over a base variety $B$ , the essential dimension of the geometric fibers may drop on a countable union of Zariski closed subsets of $B$ and stays constant away from this countable union. We give several applications of this result.

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专业化条件下本质维度的行为

设G是一个域上的线性代数群。我们证明，在温和的假设下，在基变种B上的一个原始一般自由G-变种族中，几何纤维的本质维数可能落在B的Zariski闭子集的可数并集上，并且远离该可数并并集保持不变。我们给出了这个结果的几个应用。

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

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.