an:01512803
Zbl 0963.30027
Imayoshi, Yoichi; Ito, Manabu; Yamamoto, Hiroshi
Monodromy of a holomorphic family of Riemann surfaces
EN
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).
2000
a
30F10
Authors' abstract: We consider holomorphic families of Riemann surfaces which are constructed from K??daira 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 K??daira surface due to Riera. Proofs will appear elsewhere.
For the entire collection see [Zbl 0943.00051].
Steffen Timmann (Hannover)