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Orbifolds and finite group representations. (English) Zbl 1065.14018
Summary: We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We 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 the 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.

MSC:
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14C05 Parametrization (Chow and Hilbert schemes)
14J17 Singularities of surfaces or higher-dimensional varieties
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