主极化阿贝尔变种的光滑群

IF 0.6 4区数学 Q3 MATHEMATICS Moscow Mathematical Journal Pub Date : 2019-01-21 DOI:10.17323/1609-4514-2022-22-2-225-237

Robert Auffarth, G. Arteche

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引用次数: 0

摘要

我们给出了所有主极化阿贝尔变体$（A，\Theta）$的显式刻画，使得存在$A$的自同构$G$的有限子群，其保留了$\Theta$的数值类，并且使得商变体$A/G$是光滑的。我们还给出了Jacobian曲线的光滑商的一个完整分类。

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Smooth Quotients of Principally Polarized Abelian Varieties

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numerical class of $\Theta$, and such that the quotient variety $A/G$ is smooth. We also give a complete classification of smooth quotients of Jacobian varieties of curves.

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.