Orbifolds and Finite Group Representations

Details Orbifolds and Finite Group Representations Orbifolds and Finite Group Representations

2000-07-12

arxiv.org/abs/math/0007072v3

Int.J.Math.Math.Sci. 26 (2001) 649-670

Mathematics

Algebraic Geometry

20 pages, Latex, 26 figures including 24 postscript; minor changes for clearer presentation, references updated, typos correct

Scientific paper

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We shall concern only the quotient singularity of hypersurface type. The abelian group $A_r(n)$ for $A$-type hypersurface quotient singularity of dimension $n$ is introduced. For $n=4$, the structure of Hilbert scheme of group orbits and crepant resolutions of $A_r(4)$-singularity are obtained. The flop procedure of 4-folds is explicitly constructed through the process.

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