Tokyo Journal of Mathematics

Splittability of Stellar Singular Fiber with Three Branches

Kazushi Ahara and Shigeru Takamura

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Abstract

We are concerned with the splittability problem of degenerations with stellar singular fibers. In this paper we give an interesting splitting criterion for such degenerations: if a stellar singular fiber has exactly three branches, and its central component (core) is the projective line, then this degeneration admits a splitting deformation.

Article information

Source
Tokyo J. Math., Volume 29, Number 1 (2006), 1-17.

Dates
First available in Project Euclid: 20 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1166661864

Digital Object Identifier
doi:10.3836/tjm/1166661864

Mathematical Reviews number (MathSciNet)
MR2258269

Zentralblatt MATH identifier
1102.14006

Subjects
Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
Secondary: 14J15: Moduli, classification: analytic theory; relations with modular forms [See also 32G13]

Citation

Ahara, Kazushi; Takamura, Shigeru. Splittability of Stellar Singular Fiber with Three Branches. Tokyo J. Math. 29 (2006), no. 1, 1--17. doi:10.3836/tjm/1166661864. https://projecteuclid.org/euclid.tjm/1166661864


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References

  • Ahara K., Splitica (software for Windows) http://www.geocities.co.jp/CollegeLife-Labo /9021/|,
  • Takamura, S., Towards the classification of atoms of degenerations I, Journal of Math. Soc. of Japan, to, appear.
    Mathematical Reviews (MathSciNet): MR2254876
    Zentralblatt MATH: 1100.14020
  • Takamura, S., Towards the classification of atoms of degenerations II, preprint.
    Mathematical Reviews (MathSciNet): MR2254876
    Zentralblatt MATH: 1100.14020
  • Takamura, S., Towards the classification of atoms of degenerations III, preprint.
    Mathematical Reviews (MathSciNet): MR2254876
    Zentralblatt MATH: 1100.14020
  • Takamura, S., Towards the classification of atoms of degenerations IV, preprint.
    Mathematical Reviews (MathSciNet): MR2254876
    Zentralblatt MATH: 1100.14020
  • Takamura, S., Degenerations of complex curves and construction of splitting families, (in Japanese), Mini-conference on Algebraic Geometry at Saitama University, (2000).

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Tokyo Journal of Mathematics

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