The Weierstrass semigroup of an m-tuple of collinear points on a Hermitian curve

Abstract

We examine the structure of the Weierstrass semigroup of an m-tuple of points on a smooth, projective, absolutely irreducible curve X over a finite field double-struck F sign. A criteria is given for determining a minimal subset of semigroup elements which generate such a semigroup where 2 ≤ m ≤| double-struck F sign |. For all 2 ≤ m ≤ q + 1, we determine the Weierstrass semigroup of any m-tuple of collinear double-struck F sign q2-rational points on a Hermitian curve yq + y = xq+1. © Springer-Verlag Berlin Heidelberg 2004.