,Field Theory for Function Fields of Plane Quintic Curves

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We study the structure of function fields of plane curves following our method developed in [3]. Let K be the function field of a smooth plane curve C.Let Km be a g-maximal rational subfield of K. Then the field extension K/Km is obtained by the projection from C to a line with center P ∈ C. By using this fact, we study the field extension K/Km from a geometrical viewpoint. In this paper, we treat quintic curves as a continuation of [3, 4].
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