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Acta Mathematica Vietnamica

Normal Reduction Numbers for Normal Surface Singularities with Application to Elliptic Singularities of Brieskorn Type

Tomohiro Okuma , icon-email Kei-ichi Watanabe , Ken-ichi Yoshida

Abstract

In this paper, we give a formula for normal reduction number of an integrally closed m-primary ideal of a two-dimensional normal local ring (A,m) in terms of the geometric genus pg(A) of A. Also, we compute the normal reduction number of the maximal ideal of Brieskorn hypersurfaces. As an application, we give a short proof of a classification of Brieskorn hypersurfaces having elliptic singularities.