McKay correspondence and Hilbert schemes in dimension three
| dc.creator | Ito, Yukari | |
| dc.creator | Nakajima, Hiraku | |
| dc.date | 1998-03-25 | |
| dc.date.accessioned | 2026-07-07T05:24:11Z | |
| dc.date.available | 2026-07-07T05:24:11Z | |
| dc.description | Let $G$ be a nontrivial finite subgroup of $\SL_n(\C)$. Suppose that the quotient singularity $\C^n/G$ has a crepant resolution $π\colon X\to \C^n/G$ (i.e. $K_X = \shfO_X$). There is a slightly imprecise conjecture, called the McKay correspondence, stating that there is a relation between the Grothendieck group (or (co)homology group) of $X$ and the representations (or conjugacy classes) of $G$ with a ``certain compatibility'' between the intersection product and the tensor product (see e.g. \cite{Maizuru}). The purpose of this paper is to give more precise formulation of the conjecture when $X$ can be given as a certain variety associated with the Hilbert scheme of points in $\C^n$. We give the proof of this new conjecture for an abelian subgroup $G$ of $\SL_3(\C)$. | |
| dc.description | 35 pages, 6 figures, latex2e with amsart, graphics, epic and eepic | |
| dc.identifier | https://arxiv.org/abs/math/9803120 | |
| dc.identifier | http://arxiv.org/abs/math/9803120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76742 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14E15;14E45;14E05;13D15;32S05;20C05 | |
| dc.title | McKay correspondence and Hilbert schemes in dimension three | |
| dc.type | text |