Cohomology of ideals in elliptic surface singularities

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 $1$.

15 pages; various corrections and improvements. To appear in Illinois J. Math

References in corpus (2)

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

Cited by in corpus (5)

• 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
• The normal reduction number of two-dimensional cone-like singularities
• Gorensteinness for normal tangent cones of elliptic ideals
• Normal reduction numbers of normal surface singularities