Hilbert Schemes, Separated Variables, and DBranes
Abstract
We explain Sklyanin's separation of variables in geometrical terms and construct it for Hitchin and Mukai integrable systems. We construct Hilbert schemes of points on T^{*}Σ for Σ=C, C^{*} or elliptic curve, and on C^{2}/Γ and show that their complex deformations are integrable systems of CalogeroSutherlandMoser type. We present the hyperkähler quotient constructions for Hilbert schemes of points on cotangent bundles to the higher genus curves, utilizing the results of Hurtubise, Kronheimer and Nakajima. Finally we discuss the connections to physics of Dbranes and string duality.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/s002200100503
 arXiv:
 arXiv:hepth/9901089
 Bibcode:
 2001CMaPh.222..299G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 harvmac, 27 pp. big mode