Subordinate fibers of Takamura splitting families for stellar singular fibers. (English) Zbl 1155.14008

Ahara, Kazushi; Awata, Ikuko

J. Math. Soc. Japan 60, No. 4, 983-1007 (2008).

A degeneration of Riemann surfaces of genus \(g\) is a proper holomorphic map from a smooth complex surface to the unit open disk, the fibre over the origin being singular and the other fibres being smooth curves of genus \(g\geq 1\). The authors study deformations of degenerations, i.e. splitting families of such. Their theory has been developed by Takamura. In a Takamura splitting family there are two kinds of singular fibres, a main one and subordinate ones. In this paper, when the original singular fibre is stellar and the core is a projective line, the authors determine the number of subordinate fibres and describe the types of singular points which are nodes.

Reviewer: Vladimir P. Kostov (Nice)

MSC:

14D05	Structure of families (Picard-Lefschetz, monodromy, etc.)
14J15	Moduli, classification: analytic theory; relations with modular forms
14H15	Families, moduli of curves (analytic)
32S30	Deformations of complex singularities; vanishing cycles

Keywords:

degeneration of complex curves; Riemann surface; splitting families of degenerations

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