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Normal Reduction Numbers for Normal Surface Singularities with Application to Elliptic Singularities of Brieskorn Type
Tomohiro Okuma
,
Kei-ichi Watanabe
,
Ken-ichi Yoshida
Abstract
In this paper, we give a formula for normal reduction number of an integrally closed $\mathfrak{m}$-primary ideal of a two-dimensional normal local ring $(A,\mathfrak{m})$ in terms of the geometric genus $p_g(A)$ 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.