Field theory for function fields of singular plane quartic curves

Author:

Miura Kei

Abstract

We study the structure of function fields of plane quartic curves by using projections. Taking a point P ∈ ℙ2, we define the projection from a curve C to a line l with the centre P. This projection induces and extension field k (C)/k (ℙ1). By using this fact, we study the field extension k (C)/k (ℙ1) from a geometrical point of view. In this note, we take up quartic curves with singular points.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A criterion for the existence of a plane model with two inner Galois points for algebraic curves;Hiroshima Mathematical Journal;2021-07-01

2. Automorphism group of plane curve computed by Galois points, II;Proceedings of the Japan Academy, Series A, Mathematical Sciences;2018-06-01

3. Galois Group at Each Point for Some Self-Dual Curves;Geometry;2013-01-30

4. A note on birational transformations belonging to Galois points;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2012-02-01

5. Singular plane curves with infinitely many Galois points;Journal of Algebra;2010-01

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