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arXiv · 1212.1675

The dual complex of singularities

Tommaso de Fernex·János Kollár·Chenyang Xu
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Abstract

The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal" representative of the homotopy class that is well defined up-to piecewise linear homeomorphism. This is derived from a more global result concerning dual complexes of dlt pairs. As an application, we also show that the dual complex of a log terminal singularity as well as the one of a simple normal crossing degeneration of a family of rationally connected manifolds are contractible.

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Tommaso de Fernex, János Kollár, Chenyang Xu. 2012-12-07. The dual complex of singularities. https://arxiv.org/abs/1212.1675

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