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Perverse bundles and Calogero–Moser spaces

Published online by Cambridge University Press:  01 November 2008

David Ben-Zvi
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712-0257, USA (email: [email protected])
Thomas Nevins
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (email: [email protected])
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Abstract

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We present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2008