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Monodromy of a holomorphic family of Riemann surfaces. (English) Zbl 0963.30027
Kajiwara, Joji (ed.) et al., Finite or infinite dimensional complex analysis. Proceedings of the seventh international colloquium, Fukuoka, Japan, 1999. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 214, 169-177 (2000).
Authors’ abstract: We consider holomorphic families of Riemann surfaces which are constructed from Kōdaira surfaces. Our chief interest is to classify elements of the monodromy group of such a holomorphic family of Riemann surfaces, i.e., surface automorphisms \(f_C\) on a fiber induced under the deformation of markings along closed curves \(C\) of the base surface. We will show that the Nielsen-Thurston-Bers type of \(f_C\) is described in terms of \(C\). The problem considered, and the form of the solution are suggested by Kra’s beautiful theorem on the classification of some self-maps of Riemann surfaces. In this note, we report results on the case of an example of a Kōdaira surface due to Riera. Proofs will appear elsewhere.
For the entire collection see [Zbl 0943.00051].
30F10 Compact Riemann surfaces and uniformization