Field of moduli and generalized fermat curves

A generalized Fermat curve of type (p,n) is a closed Riemann surface S admitting a group H \cong Zpn of conformal automorphisms with S/H being the Riemann sphere with exactly n+1cone points, each one of order p. If (p-1)(n-1) ≥ 3, then S is known to be non-hyperelliptic and generically not quasiplatonic. Let us denote by AutH(S) the normalizer of H in Aut(S). If p is a prime, and either (i) n=4 or (ii) n is even and AutH(S)/H is not a non-trivial cyclic group or (iii) nis odd and AutH(S)/H is not a cyclic group, then we prove that S can be defined over its field of moduli. Moreover, if n ε {3,4}, then we also compute the field of moduli of S.

• Autores: Hidalgo, Ruben A.; Reyes-Carocca, Sebastián; Valdés, María Elisa
• Tipo de recurso: Article of journal
• Fecha de publicación: 2013
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/49344
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/49344; http://bdigital.unal.edu.co/42801/
• Palabra clave: Curvas algebraicas; superficies de Riemann; cuerpo de moduli; cuerpo de definición; 14H37; 14H10; 14H45; 30F10; Algebraic curves; Riemann surfaces; Field of moduli; Field of definition
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional