Abstract

This paper presents algorithms for the identification and resolution of rational and non-rational singularities (by means of blowings-up) of a projective plane curve C: F(x 1, x 2, x 3)=0 with coefficients in a finite field k. As a result, the genus of the curve is computed. In addition the running time of the algorithms are also analyzed.Key words and phrasesfinite fieldrational pointsnon-rational pointssingular pointsblowing-up processgenus

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