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

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.

14 pages

References in corpus (3)

• Rees algebras and $p_g$-ideals in a two-dimensional normal local domain
• A characterization of two-dimensional rational singularities via Core of ideals
• Cohomology of ideals in elliptic surface singularities

Cited by in corpus (5)

• Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
• The normal reduction number of two-dimensional cone-like singularities
• Gorensteinness for normal tangent cones of elliptic ideals
• Eakin-Sathaye type theorems for joint reductions and good filtrations of ideals
• Normal reduction numbers of normal surface singularities