某平面曲线正特性对偶曲线的奇异性

IF 0.4 4区数学 Q4 MATHEMATICS

Kodai Mathematical Journal Pub Date : 2020-02-25 DOI:10.2996/kmj44110

K. Komeda

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引用次数: 0

摘要

众所周知，复平面曲线的高斯映射是对偶的，而正特性的高斯映射并不总是对偶的。设$q$是一个素数的幂。我们研究了一个次为$q^2+q+1$的平面曲线，其中高斯映射与不可分次$q$是不可分的。作为一个特例，我们给出了阶为$q^2+q+1$的Fermat曲线的对偶曲线与Ballico-Hefez曲线之间的关系。

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Singularities of the dual curve of a certain plane curve in positive characteristic

It is well known that the Gauss map for a complex plane curve is birational, whereas the Gauss map in positive characteristic is not always birational. Let $q$ be a power of a prime integer. We study a certain plane curve of degree $q^2+q+1$ for which the Gauss map is inseparable with inseparable degree $q$. As a special case, we show a relation between the dual curve of the Fermat curve of degree $q^2+q+1$ and the Ballico-Hefez curve.

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来源期刊

Kodai Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.