The dual complex of singularities

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.

21 pages; v3: final version, to appear in Adv. Stud. Pure Math., Professor Kawamata's 60th birthday volume

References in corpus (1)

• New examples of terminal and log canonical singularities

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