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Combinatorial structure of exceptional sets in resolutions of singularities

D. A. Stepanov
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Abstract

The dual complex can be associated to any resolution of singularities whose exceptional set is a divisor with simple normal crossings. It generalizes to higher dimensions the notion of the dual graph of a resolution of surface singularity. The homotopy type of the dual complex does not depend on the choice of a resolution and thus can be considered as an invariant of singularity. In this preprint we show that the dual complex is homotopy trivial for resolutions of 3-dimensional terminal singularities and for resolutions of Brieskorn singularities. We also review our earlier results on resolutions of rational and hypersurface singularities.

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BibTeXRIS

D. A. Stepanov. 2006-11-29. Combinatorial structure of exceptional sets in resolutions of singularities. https://arxiv.org/abs/math/0611903

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