Hilbert schemes, separated variables, and D-Branes

A. Gorsky, N. Nekrasov, V. Rubtsov

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

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 C2/Γ and show that their complex deformations are integrable systems of Calogero-Sutherland-Moser 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 D-branes and string duality.

Original languageEnglish
Pages (from-to)299-318
Number of pages20
JournalCommunications in Mathematical Physics
Volume222
Issue number2
DOIs
Publication statusPublished - Sep 2001
Externally publishedYes

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