Computation of Jeffrey-Kirwan residue using Gr\"obner basis

TL;DR

This paper introduces an algorithm leveraging Gr"obner bases to compute the Jeffrey-Kirwan residue, facilitating calculations of intersection numbers and symplectic quotient volumes.

Contribution

It presents a novel algorithm for Jeffrey-Kirwan residue computation using Gr"obner bases, extending prior methods for Grothendieck residues.

Findings

Algorithm successfully computes Jeffrey-Kirwan residues.

Parallel to Cattani-Dickenstein's work on Grothendieck residues.

Enhances computational tools for symplectic geometry.

Abstract

The Jeffrey-Kirwan residue is a powerful tool for computation of intersection numbers or volume of symplectic quotients. In this article, we give an algorithm to compute it using Gr\"obner bases. Our result is parallel to that of Cattani-Dickenstein for Grothendieck residues.