Perverse bundles and Calogero–Moser spaces

Publisher： Cambridge University Press

E-ISSN： 1570-5846|144|6|1403-1428

ISSN： 0010-437x

Source： Compositio Mathematica, Vol.144, Iss.6, 2008-11, pp. : 1403-1428

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Abstract

We present a simple description of moduli spaces of torsion-free -modules (-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 -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 -modules on X by a noncommutative version of the Beilinson transform on P1.

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