The reciprocal complement of a curve

TL;DR

This paper provides a geometric interpretation of the reciprocal complement of an integral domain that is a one-dimensional finitely generated algebra over an algebraically closed field.

Contribution

It introduces a new geometric perspective on the reciprocal complement for a specific class of algebraic structures.

Findings

Geometric interpretation of reciprocal complement for certain algebraic domains

Application to one-dimensional finitely generated algebras over algebraically closed fields

Enhanced understanding of the structure of integral domains in algebraic geometry

Abstract

We give a geometric interpretation of the reciprocal complement of an integral domain $D$ in the case $D$ is a one-dimensional finitely generated algebra over an algebraically closed field.