Fundamental groups of links of isolated singularities

2011/09/19 by Michael Kapovich, Janós Kollár, Kapovich, Michael +1
Mathematics · #14B05 #14F35 #14J17 #20F05 #53C55 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1109.4047

openalex publication_date 2011/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G there is a complex projective surface S with simple normal crossing singularities only, so that the fundamental group of S is isomorphic to G. We use this to construct 3-dimensional isolated complex singularities so that the fundamental group of the link is isomorphic to G. Lastly, we prove that a finitely-presented group G is Q-superperfect (has vanishing rational homology in dimensions 1 and 2) if and only if G is isomorphic to the fundamental group of the link of a rational 6-dimensional complex singularity.

Citations

• New examples of terminal and log canonical singularities

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