A Construção do espaço de Moduli de curvas pontuadas com o semigrupo de Welerstrass simétrico através do método de Stohr - O caso Trigonal

Abstract

The objective of this monograph is to try to adapt algorithmic techniques created by Stohr for the case of the irreducible projective Gorenstein curves with symmetric and trigonal semigroup, by verifying some concrete examples. This work consists of the chapters described below. In chapter 1, assuming C an irreducible, projective Gorenstein and non-hypereliptic curve, we identify such curves with its image by canonical dive and make explicit monomial bases for the space of holomorph differentials of order n. In chapter 2, we explain the canonical ideal of curve C by obtaining Grobner's bases and thus obtain the explicit equations for the moduli space for the irreducible canonical curves punctuated with this prescribed semigroup. In chapter 3, we will analyze examples, using the adopted method, of constructing the moduli space for irreducible, non-singular, projective Gorenstein curves in the trigonal case.