2000/09/21 by Kazuhiko Koike, K. Koike, Koike, K.
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG
paper · pdf · doi:10.48550/arxiv.math/0009200
latex2e + amsart
arxiv created 2000/09/21 · openalex publication_date 2000/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the inverse of the period map for the family F of complex algebraic curves of genus 6 equipped with an automorphism of order 5. This is a family with 2 parameters, and is fibred over a certain type of Del Pezzo surace. The period satisfies the hypergeometric differential equation for Appell's F1(3/5,3/5,2/5,6/5) of two variables after a certain normalization of the variable parameter. This differential equation and the family F are studied by G. Shimura (1964), T. Terada (1983, 1985), P. Deligne - G.D. Mostow (1986) and T. Yamazaki- M. Yoshida(1984). Recently M. Yoshida presented a new approch using the concept of configration space. Based on their results we show the representation of the inverse of the period map in terms of Riemann theta constants. This is the first variant of the work of H. Shiga (1981) and K. Matsumoto (1989, 2000) to the co-compact case.