Resumen de Calogero–Moser spaces over algebraic curves
In these notes, we give a survey of the main results of [5] and [7]. Our aim is to generalize the geometric classification of (left) ideals of the first Weyl algebra A1(C) (see [8, 9]) to the ring D(X) of differential operators on an arbitrary complex smooth affine curve X. We approach this problem in two steps: first, we classify the ideals of D(X) up to stable isomorphism, in terms of the Picard group of X; then, we refine this classification by describing each stable isomorphism class as a disjoint union of (quotients of) generalized Calogero–Moser spaces Cn(X,I) . The latter are defined as representation varieties of deformed preprojective algebras over a certain noncommutative extension of the ring of regular functions on X. As in the classical case, Cn(X,I) turn out to be smooth irreducible varieties of dimension 2n.
