On the family of pentagonal curves of genus 6 and associated modular forms on the ball. (English) Zbl 1038.14010
The author studies the inverse period map for the family \(F\) of complex algebraic curves of genus 6 equipped with an automorphism of order 5 having 5 fixed points. This is a 2-dimensional family over a Del Pezzo surface. The inverse period map is represented in terms of Riemann theta constants. The article is of computational nature.
Reviewer: Martin J. Pikaart (Delft)
MSC:
| 14H15 | Families, moduli of curves (analytic) |
| 11F55 | Other groups and their modular and automorphic forms (several variables) |
| 14H42 | Theta functions and curves; Schottky problem |
| 32G20 | Period matrices, variation of Hodge structure; degenerations |
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 14K25 | Theta functions and abelian varieties |
| 14H37 | Automorphisms of curves |
