Computation of Jeffrey–Kirwan residues using Gröbner bases. (March 2017)

• Record Type: Journal Article
• Authors: Szilágyi, Zsolt
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 327
• Page End: 341
• Publication Date: 2017-03
• Subjects: Jeffrey–Kirwan residue -- Gröbner basis; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.011
• Languages: English
• ISSNs: 0747-7171

Abstract

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 ofCattani and Dickenstein (2005) for Grothendieck residues.