2006/09/30 by Johan Martens
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometry and complex manifolds #hep-th #math.AG #math.SG #msc:53D20 #msc:53Z05
paper · pdf · doi:10.1007/s00220-008-0501-x
published as Commun.Math.Phys.281:827-857,2008 · 34 pages, 2 figures; minor typos corrected, to appear in Comm. Math. Phys
arxiv created 2007/10/23 · openalex publication_date 2008/05/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-Kähler geometry by means of the Jeffrey-Kirwan residue-formula of non-abelian localization. In order to overcome the non-compactness, we use varying symplectic cuts to reduce the problem to a compact setting, and study what happens in the limit that recovers the original problem. We implement this method for the ADHM construction of the moduli spaces of framed Yang-Mills instantons on \R4 and rederive the formulas for the equivariant volumes obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated residues of a single rational function.