Pontos singulares e pontos de Galois de quárticas planas singulares

Abstract

In this work we study singular plane projective curves of degree four and its Galois points. For this, we fix k, an algebraically closed field of characteristic zero, as the ground field of our discussion. To understand the structure of the function fields of these curves, we use projections: we choose a point P ? P 2 and we project a curve C ? P 2 to a line from P, that is the center of projection. This projection induces an extension field k(C) | k(P 1 ), where k(C) is the rational function field of C. We want to know if there exist intermediate fields in this extension. We analyse two situations: P belongs to the curve C and P doesn’t belong to C