Divisor interseção de uma curva mergulhada canonicamente com seus espaços osculadores

Abstract

Let C a non-singular algebraic curve, irredutible and non-hipereliptic over a closed algebrically field K. In this work we to deal of a result geometric to such curve. This result to be introduced in the theorem three and say us that the intersection divisors of a curve C canonically embedded with its osculating spaces at a point P, not considering the intersection at P, can vary only in dimensions given by the Weierstrass semigroup of the curve C at P. Under a reasonable geometrical hypothesis, we to obtain monomial basis for the spaces of higher-order regular differentials (theorem four). Afterwards, in the proposition fifteen,to going a condition on the Weierstrass semigroup of curve C at P in order for this geometrical hipothesis to be true. Finally, we will give examples ofWeierstrass semigroups satisfying such condition.