Perverse Bundles and Calogero-Moser Spaces

David Ben-Zvi; Thomas Nevins

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arXiv · math/0610097

Perverse Bundles and Calogero-Moser Spaces

David Ben-Zvi·Thomas Nevins

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Abstract

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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David Ben-Zvi, Thomas Nevins. 2007-11-01. Perverse Bundles and Calogero-Moser Spaces. https://arxiv.org/abs/math/0610097

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