Geometrical McKay Correspondence for Isolated Singularities

2003/02/06 by Anda Degeratu, Degeratu, Anda
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #hep-th #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.math/0302068

25 pages added references; corrected typos

openalex publication_date 2003/02/06 · arxiv created 2003/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Calabi-Yau orbifold is locally modeled on Cⁿ/G where G is a finite subgroup of SL(n, C). In dimension n=3 a crepant resolution is given by Nakamura's G-Hilbert scheme. This crepant resolution has a description as a GIT/symplectic quotient. We use tools from global analysis to give a geometrical generalization of the McKay Correspondence to this case.

Citations

• The mass of an asymptotically flat manifold
• McKay correspondence

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• On the topology of desingularizations of Calabi-Yau orbifolds
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