The dual complex of singularities
Algebraic Geometry
2014-03-18 v3
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.
Cite
@article{arxiv.1212.1675,
title = {The dual complex of singularities},
author = {Tommaso de Fernex and János Kollár and Chenyang Xu},
journal= {arXiv preprint arXiv:1212.1675},
year = {2014}
}
Comments
21 pages; v3: final version, to appear in Adv. Stud. Pure Math., Professor Kawamata's 60th birthday volume