Cohomology of ideals in elliptic surface singularities

2018/04/20 by Tomohiro Okuma, Okuma, Tomohiro · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 14J17 #Secondary 14B05

paper · pdf · doi:10.48550/arxiv.1804.07558

openalex publication_date 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the the normal reduction number of two-dimensional normal singularities and prove that elliptic singularity has normal reduction number two. We also prove that for a two-dimensional normal singularity which is not rational, it is Gorenstein and its maximal ideal is a p_g-ideal if and only if it is a maximally elliptic singularity of degree 1.

Citations

• Rees algebras and p_g-ideals in a two-dimensional normal local domain

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 for normal surface singularities with application to elliptic singularities of Brieskorn type
• Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
• Good ideals and p_g-ideals in two-dimensional normal singularities
• Gorensteinness for normal tangent cones of elliptic ideals
• A characterization of two-dimensional rational singularities via Core of ideals