Perverse Bundles and Calogero-Moser Spaces

Details Perverse Bundles and Calogero-Moser Spaces Perverse Bundles and Calogero-Moser Spaces

2006-10-03

arxiv.org/abs/math/0610097v2

Mathematics

Algebraic Geometry

v2: Expanded exposition, including additional background and references on DG categories

Scientific paper

We present a simple description of moduli spaces of torsion-free D-modules (``D-bundles'') on general smooth complex curves X, 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 stacks 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 the projective line.

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