2017/05/25 by Rubén A. Hidalgo, Hidalgo, Ruben A.
Mathematics · #30F10 #30F40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1705.09337
openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A group H ≅ \mathbb Z2n, n ≥ 3, of conformal automorphisms of a closed Riemann surface S such that S/H has genus zero and exactly (n+1) cone points is called a generalized Humbert group of type n, in which case, S is called a generalized Humbert curve of type n. It is known that a generalized Humbert curve S of type n ≥ 4 is non-hyperelliptic and that it admits a unique generalized Humbert group H of type n. We describe those subgroups K of H, acting freely on S, such that S/K is hyperelliptic.