2007/05/22 by Lev Birbrair, Birbrair, Lev, Alexandre Fernandes +1
Mathematics · #14P10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.AT #msc:14P10
paper · pdf · doi:10.48550/arxiv.0705.3185
12 pages
arxiv created 2007/05/22 · openalex publication_date 2007/05/22 · arxiv updated 2009/12/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to the inner metric, to cones. The technique used to prove the nonexistence of the metric conic structure is related to a development of Metric Homology. The class of the examples is rather large and it includes some surfaces of Brieskorn.