Equivariant Jeffrey-Kirwan localization theorem in non-compact setting

Autor:	Szilágyi, Zsolt
Rok vydání:	2013
Předmět:	Mathematics - Symplectic Geometry Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 46 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1302.6864 Zobrazit plný text záznamu View this record from Arxiv