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Function field theory of plane curves by dual curves. (English) Zbl 1064.14023
Summary: We study the structure of function fields of plane curves following our method developed previously in a joint paper with K. Miura [J. Algebra 226, 283–294 (2000; Zbl 0983.11067)]. Let \(K\) be the function field of a smooth plane curve \(C\) of degree \(d\geq 4\) and let \(K_P\) be a maximal rational subfield of \(K\) for \(P\in \mathbb{P}^2\). We study the field extension \(K/K_P\) from a geometrical viewpoint. Especially, we give a sufficient condition that the Galois group of the Galois closure of \(K/K_P\) becomes a full symmetric group.

14H05 Algebraic functions and function fields in algebraic geometry
12F10 Separable extensions, Galois theory
14H50 Plane and space curves
Full Text: DOI
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