Sets of values of fractional ideals of rings of algebroid curves

TL;DR

This paper investigates the structure and symmetry of value sets of fractional ideals in rings of algebroid curves, especially focusing on Gorenstein rings, and relates these properties to codimensions and duality.

Contribution

It provides new insights into the symmetry of value sets of dual ideals in Gorenstein rings and characterizes Gorensteinness through codimension conditions.

Findings

Symmetry among value sets of dual ideals in Gorenstein rings

Expression of codimension of fractional ideals via maximal points

Gorenstein property characterized by codimension conditions

Abstract

The aim of this work is to study sets of values of fractional ideals of rings of algebroid curves and explore more deeply the symmetry that exists among sets of values of dual pairs of ideals when the ring is Gorenstein. We also express the codimension of a fractional ideal in terms of the maximal points of the value set of the ideal. Finally we also show that the Gorensteiness of a ring of an algebroid curve is equivalent to some conditions relating certain codimensions of fractional ideals and of their duals.