On Fields of Definition of an Algebraic Curve

被引：0

作者：

Smirnov A.L. ^{[1
]}

机构：

[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg

来源：

Journal of Mathematical Sciences | 2016年 / 219卷 / 3期

关键词：

D O I：

10.1007/s10958-016-3121-6

中图分类号：

学科分类号：

摘要：

The paper deals with geometric invariants of an algebraic curve such as the minimal number of crucial values of rational functions and the minimal transcendence degree of definition fields. The main question is if the difference of these two invariants is always equal to 3 for any curve with genus g > 0. For curves defined over an algebraic number field, a positive answer is given by Belyi’s theorem. In the paper, the main question is answered in the affirmative for some other cases. © 2016, Springer Science+Business Media New York.

引用

页码：484 / 491

页数：7

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