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

Authors :
Okuma, Tomohiro
Watanabe, Kei-ichi
Yoshida, Ken-ichi
Publication Year :
2018

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.<br />Comment: 14 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1804.03795
Document Type :
Working Paper