Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems
Complex Variables
2012-04-11 v2 Algebraic Geometry
General Topology
Abstract
In this paper, we construct holomorphic families of Riemann surfaces from Veech groups and characterize their sections by some points of corresponding flat surfaces. The construction gives us concrete solutions for some Diophantine equations over function fields. Moreover, we give upper bounds of the numbers of holomorphic sections of certain holomorphic families of Riemann surfaces.
Keywords
Cite
@article{arxiv.1202.5002,
title = {Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems},
author = {Yoshihiko Shinomiya},
journal= {arXiv preprint arXiv:1202.5002},
year = {2012}
}
Comments
28 pages; Exposition improved. New results are added