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

Yuri Berest·Oleg Chalykh
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Abstract

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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Yuri Berest, Oleg Chalykh. 2004-10-06. $A_{\infty}$-modules and Calogero-Moser Spaces. https://arxiv.org/abs/math/0410194

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