The fundamental group of Galois covers of surfaces with octahedral envelope

2023/03/09 by Meirav Amram, Amram, Meirav, Gong Cheng +7
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2303.05241

openalex publication_date 2023/03/09 · openalex created_date 2023/03/12 · openalex updated_date 2026/07/28

Abstract

We compute the fundamental group of the Galois cover of a surface of degree~8, with singularities of degree 4, whose degeneration envelope is isomorphic to an octahedron. The group is shown to be a metabelian group of order 2²³. The computation amalgamates local groups, classified elsewhere, by an iterative combination of computational and group theoretic methods. Three simplified surfaces, for which the fundamental group of the Galois cover is trivial, demonstrate how nontrivial cycles in the degenerated surface complicate the computation.

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