Journal of the Mathematical Society of Japan

Subordinate fibers of Takamura splitting families for stellar singular fibers

Kazushi AHARA and Ikuko AWATA

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Abstract

Takamura constructed a theory on splitting families of degenerations of Riemann surfaces. We call them Takamura splitting families. In a Takamura splitting family, there appear two kinds of singular fibers, called a main fiber and subordinate fibers. In this paper, when the original singular fiber is stellar and the core is a projective line, we determine the number of subordinate fibers and describe the types of singular points, which are nodes.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 983-1007.

Dates
First available in Project Euclid: 5 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1225894030

Digital Object Identifier
doi:10.2969/jmsj/06040983

Mathematical Reviews number (MathSciNet)
MR2467867

Zentralblatt MATH identifier
1155.14008

Subjects
Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14J15: Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
Secondary: 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 32S30: Deformations of singularities; vanishing cycles [See also 14B07]

Keywords
degeneration of complex curves Riemann surface splitting families of degenerations

Citation

AHARA, Kazushi; AWATA, Ikuko. Subordinate fibers of Takamura splitting families for stellar singular fibers. J. Math. Soc. Japan 60 (2008), no. 4, 983--1007. doi:10.2969/jmsj/06040983. https://projecteuclid.org/euclid.jmsj/1225894030


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References

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