Curvas algébricas planas invariantes por sistemas de equações diferenciais polinomiais: um estudo do grau-gênero das curvas invariantes.

Abstract

The main objective of this work is to present a study that determines an upper bound for the degree of algebraic projective curves that are invariant by a system of plane polynomial differential systems. In the text we make a brief study of the theory of Algebraic Geometry and Riemann Surfaces. We also present a proof of the Normalization Theorem of singular plane projective algebraic curves. The work is divided into two parts, in the first we consider smooth curves and, in the second, singular curves. Finally, we give an upper bound for the degree of a nodal algebraic plane projective curve which is invariant by a system of polynomial differential equations.