$A_{\infty}$-modules and Calogero-Moser Spaces

Details $A_{\infty}$-modules and Calogero-Moser Spaces $A_{\infty}$-modules and Calogero-Moser Spaces

2004-10-06

arxiv.org/abs/math/0410194v2

J. reine angew. Math. 607 (2007), 69-112

Mathematics

Quantum Algebra

Final version (revised, with new appendix)

Scientific paper

We re-examine the bijective correspondence between the set of isomorphism classes of ideals of the first Weyl algebra and associated quiver varieties (Calogero-Moser spaces) \cite{BW1, BW2}. We give a new explicit construction of this correspondence based on the notion of $\A$-envelope of a rank one torsion-free $A_1$-module. Though perhaps less geometric than other methods, our approach is much simpler and seems more natural from the point of view of deformation theory.

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