Quiver varieties and Hilbert schemes
| dc.creator | Kuznetsov, Alexander | |
| dc.date | 2001-11-08 | |
| dc.date.accessioned | 2026-07-07T04:44:27Z | |
| dc.date.available | 2026-07-07T04:44:27Z | |
| dc.description | In this note we give an explicit geometric description of some of the Nakajima's quiver varieties. More precisely, we show that the $Γ$-equivariant Hilbert scheme $X^{Γ[n]}$ and the Hilbert scheme $X_Γ^{[n]}$ (where $X=\C^2$, $Γ\subset SL(\C^2)$ is a finite subgroup, and $X_Γ$ is a minimal resolution of $X/Γ$) are quiver varieties for the affine Dynkin graph, corresponding to $Γ$ via the McKay correspondence, the same dimension vectors, but different parameters $ζ$ (for earlier results in this direction see [4, 12, 13]). In particular, it follows that the varieties $X^{Γ[n]}$ and $X_Γ^{[n]}$ are diffeomorphic. Computing their cohomology (in the case $Γ=\Z/d\Z$) via the fixed points of $(\C^*\times\C^*)$-action we deduce the following combinatorial identity: the number $UCY(n,d)$ of uniformly coloured in d colours Young diagrams consisting of nd boxes coincides with the number $CY(n,d)$ of collections of d Young diagrams with the total number of boxes equal to n. | |
| dc.description | LaTeX, 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111092 | |
| dc.identifier | http://arxiv.org/abs/math/0111092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62594 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Quiver varieties and Hilbert schemes | |
| dc.type | text |