Almost symmetric good semigroups

TL;DR

This paper characterizes almost symmetric good semigroups in multiple dimensions, extending classical results and applying them to gain new insights into the structure of almost Gorenstein rings.

Contribution

It extends known characterizations of symmetric semigroups to the multi-dimensional case and connects these to properties of almost Gorenstein rings.

Findings

Characterization of almost symmetric good semigroups in N^h

Extension of numerical semigroup theory results to higher dimensions

New results on almost Gorenstein one-dimensional rings

Abstract

The class of good semigroups is a class of subsemigroups of $N^h$, that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this paper we give a characterization of almost symmetric good subsemigroups of $N^h$, extending known results in numerical semigroup theory and in one-dimensional ring theory, and we apply these results to obtain new results on almost Gorenstein one-dimensional analytically unramified rings.