Eliminating dual spaces

TL;DR

This paper introduces eliminating dual spaces, a new computational tool for algebraic geometry, enabling efficient analysis of quotient ideals and detection of embedded points on algebraic curves.

Contribution

The paper presents eliminating dual spaces and an algorithm for detecting embedded points, advancing computational methods in algebraic geometry.

Findings

Efficient computation of dual spaces of quotient ideals

Algorithm for detecting embedded points on algebraic curves

Enhanced tools for local analysis of affine schemes

Abstract

Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing dual spaces of quotient ideals, and develop an algorithm for detection of embedded points on an algebraic curve.