Calogero-Moser Spaces over Algebraic Curves
| dc.creator | Berest, Yuri | |
| dc.date | 2008-09-26 | |
| dc.date.accessioned | 2026-07-07T10:05:39Z | |
| dc.date.available | 2026-07-07T10:05:39Z | |
| dc.description | In 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.description | to appear in Selecta Math., 21 pp | |
| dc.identifier | https://arxiv.org/abs/0809.4521 | |
| dc.identifier | http://arxiv.org/abs/0809.4521 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170068 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16S32; 16S38; 16G20; 14H60; 18E30 | |
| dc.title | Calogero-Moser Spaces over Algebraic Curves | |
| dc.type | text |