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

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.

Final version (revised, with new appendix)

Cited by in corpus (1)

• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models