2013/02/27 by Szilágyi, Zsolt
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1302.6864
We generalize the Jeffrey-Kirwan localization theorem for non-compact symplectic and hyperKahler quotients. Similarly to the circle compact integration of Hausel and Proudfoot we define equivariant integrals on non-compact manifolds using the Atiyah-Bott-Berline-Vergne localization formula as formal definition. We introduce a so called equivariant Jeffrey-Kirwan residue and we show that it shares similar properties as the usual one. Our localization formula has the same structure as the usual Jeffrey-Kirwan formula, but it uses formal integration and equivariant residue. We also give a version for hyperKahler quotients. Finally, we apply our formula to compute the equivariant cohomology ring of Hilbert scheme of points on the plane constructed as a hyperKahler quotient.