Monodromy groups of regular elliptic surfaces

2000/06/30 by Michael Lönne, Lönne, Michael
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0006231

15 pages

arxiv created 2000/06/30 · openalex publication_date 2000/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p_g>q=0, we determine the monodromy group of a representative X, i.e. the group of isometries of the intersection lattice L_X:=H₂/torsion generated by the monodromy action of all families containing X. To this end we construct families such that any isometry is in the group generated by their monodromies or does not respect the invariance of the canonical class or the spinor norm.

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