Computation of Jeffrey–Kirwan residues using Gröbner bases

Abstract

In this article, we give an algorithm to compute the Jeffrey–Kirwan residue. The Jeffrey–Kirwan residue is an important tool since it can be used, for instance, to determine the intersection numbers or volume of symplectic quotients. The main idea for the algorithm is to reduce the problem to that of normal form computation, which can be done via Gröbner basis. Our result is parallel to that of Cattani and Dickenstein (2005) for Grothendieck residues.