The dual complex of singularities
By Tommaso de Fernex, J. Kollár. 2012
103 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/26aa3896881e35f686a4190abb7e86d9105e94f2
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The dual complex of Calabi–Yau pairs (2015, unknown): “By [6] D =1 Y ) is independent of the choice of (Y, Y ), up-to PL-homeomorphism.”
- The essential skeleton of a degeneration of algebraic varieties (2013, methodology): “sume that m>M, so that (Y ,(Ys) red − 1 m Ys) is a kltpair. Hence, the finite generation of A follows from [BCHM10]. 6 JOHANNES NICAISE AND CHENYANG XU (2) It is already observed in Definition 15 of [dFKX12] that this follows from the proof of [KM98, 3.52]. 3. The essential skeleton 3.1. Retraction”
- Functorial tropicalization of logarithmic schemes: the case of constant coefficients (2013, methodology): “ogarithmic compactifications and can also serve as model spaces for weight zero parts of the cohomology of X−D, in case Xis defined over C. For these recent developments we refer the reader to [ABW13], [dFKX12], [Kol12], [Pay13a], and [Ste06]. 1.8. Our approach to the construction of tropX is a global”