Quasihomogene Singularitäten algebraischer Kurven

Abstract

In this note we consider algebraic curves X over an algebraically closed field k of characteristic O. We give some characterizations in terms of differentials of quasihomogeneous curve singularities, similar to well-known characterizations of quasihomogeneous isolated singularities of hypersurfaces (see [2] and the literature quoted there). Moreover, we discuss the structure of the completion Ô_X of the local ring in such singularities. In case X has at most two analytic branches in a quasihomogeneous singularity a classification of the k-algebras Ô_X up to isomorphism can be given.