Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 83-95

ON HOLOMORPHIC SECTIONS OF VEECH HOLOMORPHIC FAMILIES OF RIEMANN SURFACES

Yoshihiko Shinomiya

Tokyo Institute of Technology, Department of Mathematics
2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan; shinomiya.y.aa 'at' m.titech.ac.jp

Abstract. We give upper bounds of the numbers of holomorphic sections of Veech holomorphic families of Riemann surfaces. The numbers depend only on the topological types of the base Riemann surfaces and fibers. We also show a relation between signatures of Veech groups and moduli of cylinder decompositions of flat surfaces.

2010 Mathematics Subject Classification: Primary 32G15; Secondary 32G05, 32G08.

Key words: Holomorphic section, flat surfaces, Veech groups.

Reference to this article: Y. Shinomiya: On holomorphic sections of Veech holomorphic families of Riemann surfaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 83-95.

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doi:10.5186/aasfm.2014.3906