Good ideals and p_g-ideals in two-dimensional normal singularities

2014/07/07 by Tomohiro Okuma, Okuma, Tomohiro, Kei-ichi Watanabe +3 · 5 citations
Mathematics · #13A35 (Primary) #14B05 #14J17 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.1407.1590

openalex publication_date 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the notion of p_g-ideals and p_g-cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we prove an existence of good ideals for two-dimensional Gorenstein normal local rings. Moreover, we classify all Ulrich ideals for two-dimensional simple elliptic singularities with small degree.

Cited by

• Gorenstein Normal tangent cones of integrally closed ideals in two-dimensional normal singularities
• Hyperelliptic involutions on generic normal surface singularities
• Ulrich ideals on rational triple points of dimension two
• Invariants of relatively generic structures on normal surface\n singularities
• A characterization of two-dimensional rational singularities via Core of ideals

Related

• Ulrich ideals and modules over two-dimensional rational singularities
• A characterization of two-dimensional rational singularities via Core of ideals
• Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
• Cohomology of ideals in elliptic surface singularities
• Rees algebras and p_g-ideals in a two-dimensional normal local domain