代数变种的内射自映射

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-04-25 DOI:10.1016/j.jpaa.2025.107988

Indranil Biswas , Nilkantha Das

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引用次数: 0

摘要

Miyanishi的一个猜想说，定义在特征为0的代数闭域上的代数变量的自同构，如果自同构在至少2维的闭子集外内射，则是自同构。我们在以下情况下证明了这个猜想：(1)变种是非奇异的(2)变种是一个曲面(3)变种是一个在余维数2上正则的局部完全交。我们还讨论了几个例子，其中一个品种的自同态，满足Miyanishi猜想的假设，诱导该品种的非奇异轨迹的自同态。在附加的假设下，我们证明了当变异只有孤立的奇点时，这个猜想成立。

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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On the injective self-maps of algebraic varieties

A conjecture of Miyanishi says that an endomorphism of an algebraic variety, defined over an algebraically closed field of characteristic zero, is an automorphism if the endomorphism is injective outside a closed subset of codimension at least 2. We prove the conjecture in the following cases:

(1)
The variety is non-singular.
(2)
The variety is a surface.
(3)
The variety is locally a complete intersection that is regular in codimension 2.

We also discuss a few instances where an endomorphism of a variety, satisfying the hypothesis of the conjecture of Miyanishi, induces an automorphism of the non-singular locus of the variety. Under additional hypotheses, we prove that the conjecture holds when the variety has only isolated singularities.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.