2010/12/20 by Mariela Carvacho Bustamante, Bustamante, Mariela Carvacho
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AG
paper · pdf · doi:10.48550/arxiv.1012.4337
20 pages, 2 figures
arxiv created 2010/12/20 · openalex publication_date 2010/12/20 · arxiv updated 2010/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We produce for each natural number n ≥ 3 two 1--parameter families of Riemann surfaces admitting automorphism groups with two cyclic subgroups H1 and H2 of orden 2n, that are conjugate in the group of orientation--preserving homeomorphism of the corresponding Riemann surfaces, but not conjugate in the group of conformal automorphisms. This property implies that the subvariety Mg(H1) of the moduli space Mg consisting of the points representing the Riemann surfaces of genus g admitting a group of automorphisms topologically conjugate to H1 (equivalently to H2) is not a normal subvariety.