Open Access
VOL. 74 | 2017 The dual complex of singularities
Tommaso de Fernex, János Kollár, Chenyang Xu

Editor(s) Keiji Oguiso, Caucher Birkar, Shihoko Ishii, Shigeharu Takayama

Adv. Stud. Pure Math., 2017: 103-129 (2017) DOI: 10.2969/aspm/07410103


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.


Published: 1 January 2017
First available in Project Euclid: 23 October 2018

zbMATH: 1388.14107
MathSciNet: MR3791210

Digital Object Identifier: 10.2969/aspm/07410103

Primary: 14D06 , 14J17

Keywords: dual complex , minimal model program , singularities

Rights: Copyright © 2017 Mathematical Society of Japan


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