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

2018/04/11 by Tomohiro Okuma, Okuma, Tomohiro, Kei-ichi Watanabe +3 · 2 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1804.03795

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.

Cited by

• A variant of Röhr's vanishing theorem with an application to the normal reduction number for normal surface singularities
• Gorenstein Normal tangent cones of integrally closed ideals in two-dimensional normal singularities

Related

• Normal reduction numbers of normal surface singularities
• The normal reduction number of two-dimensional cone-like singularities
• Cohomology of ideals in elliptic surface singularities
• Normal reduction number of normal surface singularities
• A variant of Röhr's vanishing theorem with an application to the normal reduction number for normal surface singularities