Weierstraß semigroups and nodal curves of type p,q

Abstract

We study plane curves of type p, q having only nodes as singularities. Every Weierstrass semigroup is the Weierstrass semigroup of such a curve at its place at infinity for properly chosen p, q. We construct plane curves of type p,q with explicitly given nodes and determine their Weierstrass semigroups. Many such semigroups are found. (C) 2011 Elsevier Inc. All rights reserved.