Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems

Details Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems

2012-02-22

arxiv.org/abs/1202.5002v2

Mathematics

Complex Variables

28 pages; Exposition improved. New results are added

Scientific paper

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.

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