DG-models of Projective Modules and Nakajima Quiver Varieties
| dc.creator | Eshmatov, Farkhod | |
| dc.date | 2006-04-02 | |
| dc.date.accessioned | 2026-07-07T07:10:23Z | |
| dc.date.available | 2026-07-07T07:10:23Z | |
| dc.description | Associated to each finite group $Γ$ in $SL_2(C)$ there is a family of noncommutative algebras which deforms the coordinate ring of the Kleinian singularity corresponding to that group. These algebras were defined by W. Crawley-Boevey and M. Holland, who also suggested a conjectural correspondence between the set of isomorphism classes of rank one projective modules over these algebras and associated Nakajima quiver varieties. In \cite{BGK}, V.Baranovski, V.Ginzburg and A.Kuznetsov proved the Crawley-Boevey-Holland conjecture using the methods of noncommutative projective geometry. In this paper we will state a refined ($G$-equivariant) version of this conjecture and, in the case of cyclic groups, give a new construction of this correspondence based on the notion of DG-model of a rank one projective module. This construction leads to a completely explicit description of ideals of the Crawley-Boevey-Holland algebras. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604011 | |
| dc.identifier | http://arxiv.org/abs/math/0604011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111408 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | DG-models of Projective Modules and Nakajima Quiver Varieties | |
| dc.type | text |