The Classification of Hyperelliptic Groups in Dimension 4

2022/11/15 by Andreas Demleitner, Demleitner, Andreas · 1 citation
Mathematics · #14J10 #14L30 #20C15 #32Q57 (Primary) 20H15 #53C29 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.07998

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hyperelliptic manifolds are natural generalizations of hyperelliptic surfaces in dimensions. We provide a full classification of the groups, which arise as the holonomy group of a 4-dimensional hyperelliptic manifold. The classification is mostly based on group- and representation-theoretic methods.

Cited by

• On Mukai's conjecture for hyperelliptic varieties

Related

• The classification of Hyperelliptic threefolds
• Hyperelliptic Threefolds with group D₄, the Dihedral group of order 8
• Finite groups acting on hyperelliptic 3-manifolds
• The hyperelliptic mapping class group of a nonorientable surface of genus g≥ 4 has a faithful representation into GL(g²-1,ℝ)
• The 2-rank of finite groups acting on hyperelliptic 3-manifolds