Fields of definition of a family of curves

ZHOU Yun

doi:10.7523/j.issn.2095-6134.2007.6.001

Journal of University of Chinese Academy of Sciences >

2007 , Vol. 24 >Issue 6: 725 - 728

DOI: https://doi.org/10.7523/j.issn.2095-6134.2007.6.001

论文

Fields of definition of a family of curves

ZHOU Yun

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Graduate University of Chinese Academy of Sciences

Received date: 1900-01-01

Revised date: 1900-01-01

Online published: 2007-11-15

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Abstract

Let K be a finitely generated field extension of an algebraically closed
field k and C : f(x) = ayn be a curve over K, where char(k) - n, f(x) 2 k[x].
When n > 4, a 62 Kn and f has at least three simple zeros, the curve C is not defined over k.

Key words： Algebraic curves; Genus; Automorphisms

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ZHOU Yun . Fields of definition of a family of curves[J]. Journal of University of Chinese Academy of Sciences, 2007 , 24(6) : 725 -728 . DOI: 10.7523/j.issn.2095-6134.2007.6.001

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