McKay correspondence and Hilbert schemes in dimension three

dc.creatorIto, Yukari
dc.creatorNakajima, Hiraku
dc.date1998-03-25
dc.date.accessioned2026-07-07T05:24:11Z
dc.date.available2026-07-07T05:24:11Z
dc.descriptionLet $G$ 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.description35 pages, 6 figures, latex2e with amsart, graphics, epic and eepic
dc.identifierhttps://arxiv.org/abs/math/9803120
dc.identifierhttp://arxiv.org/abs/math/9803120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76742
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14E15;14E45;14E05;13D15;32S05;20C05
dc.titleMcKay correspondence and Hilbert schemes in dimension three
dc.typetext

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