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arXiv · 1804.03795

Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type

Tomohiro Okuma·Kei-ichi Watanabe·Ken-ichi Yoshida
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Abstract

In this paper, we give a formula for normal reduction number of an integrally closed $\mathfrak m$-primary ideal of a $2$-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.

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Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida. 2018-04-11. Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type. https://doi.org/10.1007/s40306-018-00311-4

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