2006/06/08 by Hiraku Nakajima, Göttsche, Lothar, Nakajima, Hiraku +2 · 2 citations
Chemistry · Physics and Astronomy · #14D21 #57R57 #81T13 #81T60 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #History and advancements in chemistry #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.math/0606180
openalex publication_date 2006/06/08 · openalex created_date 2017/04/07 · openalex updated_date 2026/07/28
For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture math.AG/0306198, hep-th/0306238, math.AG/0409441 and its refinement math.AG/0311058, we apply this result to give a generating function for the wallcrossing of Donaldson invariants of good walls of simply connected projective surfaces with b+=1 in terms of modular forms. This formula was proved earlier in alg-geom/9506018 more generally for simply connected 4-manifolds with b+=1, assuming the Kotschick-Morgan conjecture and it was also derived by physical arguments in hep-th/9709193.