Calogero-Moser Spaces over Algebraic Curves

dc.creatorBerest, Yuri
dc.date2008-09-26
dc.date.accessioned2026-07-07T10:05:39Z
dc.date.available2026-07-07T10:05:39Z
dc.descriptionIn these notes, we give a survey of the main results of [BC] and [BW]. Our aim is to generalize the geometric classification of (one-sided) ideals of the first Weyl algebra $ A_1(C) $ (see [BW1, BW2]) 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 (certain quotients of) generalized Calogero-Moser spaces C_n(X, I). The latter are defined as representation varieties of deformed preprojective algebras over a one-point extension of the ring of regular functions on X by the line bundle I. As in the classical case, C_n(X, I) turn out to be smooth irreducible varieties of dimension 2n.
dc.descriptionto appear in Selecta Math., 21 pp
dc.identifierhttps://arxiv.org/abs/0809.4521
dc.identifierhttp://arxiv.org/abs/0809.4521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170068
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject16S32; 16S38; 16G20; 14H60; 18E30
dc.titleCalogero-Moser Spaces over Algebraic Curves
dc.typetext

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