2012/12/07 by Tommaso de Fernex, Janós Kollár, de Fernex, Tommaso +3 · 9 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1212.1675
openalex publication_date 2012/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.