The semigroup of a space curve singularity

Julio Castellanos

Vol. 221 (2005), No. 2, 227–251

DOI: 10.2140/pjm.2005.221.227

Abstract

The semigroup of values of a space curve singularity is an invariant of the singularity. We analyze the complexity of this invariant, in order to describe the geometric invariants of the sequence of infinitely near points of the curve necessary to determine the generators of the semigroup. We give several approaches and examples using Hamburger–Noether matrices to describe the infinitely near points of the curve.

Keywords

curve singularities, numerical semigroups

Mathematical Subject Classification 2000

Primary: 14B05, 14H2D

Milestones

Received: 21 November 2003

Revised: 5 October 2004

Accepted: 2 November 2004

Published: 1 October 2005