Symmetry of maximals for fractional ideals of curves

TL;DR

This paper extends the symmetry properties of maximals in fractional ideals of plane curve germs to more general admissible rings, providing new characterizations of elements and duals in algebraic geometry.

Contribution

It generalizes Delgado's symmetry of maximals to broader classes of rings and relates relative maximals to absolute maximals of dual ideals.

Findings

Extended symmetry of maximals to admissible rings

Characterized elements in value sets via projections

Linked irreducible absolute maximals to dual ideals

Abstract

The purpose of this paper is to extend the symmetry of maximals of the ring of a germ of reducible plane curve proved by Delgado to a relation between the relative maximals of a fractional ideal and the absolute maximals of its dual for any admissible ring. In particular, it includes the case of germs of reduced reducible curve of any codimension. We then apply this symmetry to characterize the elements in the set of values of a fractional ideal from some of its projections and the irreducible absolute maximals of the dual ideal.