Computing the Field of moduli of some non-hyperelliptic pseudo-real curves

2024/01/10 by Rubén A. Hidalgo, Hidalgo, Ruben A.
Mathematics · #14H45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Primary 14H37 #Secondary 30F10

paper · pdf · doi:10.48550/arxiv.2401.05287

openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The explicit computation of the field of moduli of a closed Riemann surface is, in general, a difficult task. In this paper, for each even integer k ≥ 2, we consider a suitable 2-real parameter family of non-hyperelliptic pseudo-real Riemann surfaces of genus g=1+(2k-3)k⁴. For each of them, we compute its field of moduli and also a minimal field of definition.

Related

• Riemann surfaces defined over the reals
• Fields of moduli and fields of definition of curves
• Fields of Moduli of Smooth del Pezzo Surfaces
• The field of moduli of singular K3 surfaces
• Non hyperelliptic curves of genus three over finite fields of characteristic two