2016/04/27 by Jaeyoo Choy
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Combinatorics #Geometry #Instanton #Mathematical physics #Mathematics #Moduli #Moduli space #Moment map #Physics #Symplectic geometry #math-ph #math.AG #math.MP #msc:14D21 #msc:81T13
paper · pdf · doi:10.1016/j.geomphys.2016.04.011
published as J. Geom. Phys. 106 (2016) 284--304; 110 (2016), 343--347 · 32 pages, 1 figure; 7 pages (corrigendum and addendum)
openalex publication_date 2016/04/27 · openalex created_date 2016/06/24 · arxiv created 2016/09/30 · arxiv updated 2016/10/05 · openalex updated_date 2026/08/05
Let K be the compact Lie group USp(N/2) or SO(N, R). Let MKn be the moduli space of framed K-instantons over S4 with the instanton number n. By Donaldson (1984), MKn is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ-1(0), where μ is a holomorphic moment map such that μ-1(0) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ-1(0) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K=USp(N/2) then μ is flat and μ-1(0) is an irreducible normal variety for any n and even N. If K = SO(N, R) the similar results are proven for low n and N. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).