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Field theory for function fields of singular plane quartic curves

Published online by Cambridge University Press:  17 April 2009

Kei Miura
Kei Miura
Affiliation:
Graduate School of Science and Technology, Niigata University, Niigata 950–2181, Japan e-mail: kmiura@scux.sc.niigata-u.ac.jp
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 193 - 204
Copyright
Copyright © Australian Mathematical Society 2000

References

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