Monodromy groups of irregular elliptic surfaces

2000/11/08 by Michael Lönne, Lönne, Michael
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0011049

14 pages

arxiv created 2000/11/08 · openalex publication_date 2000/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Monodromy groups, i.e. the groups of isometries of the intersection lattice L_X:=H₂/torsion generated by the monodromy action of all deformation families of a given surface, have been computed in math.AG/0006231 for any minimal elliptic surface with p_g>q=0. New and refined methods are now employed to address the cases of minimal elliptic surfaces with p_g+1>q>0. To this end we find explicit 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. The monodromy action is moreover shown to act by the full symplectic group on the first homology modulo torsion.

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