Osaka Journal of Mathematics

Realization of hyperelliptic families with the hyperelliptic semistable monodromies

Mizuho Ishizaka

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Abstract

Let $\Phi$ be an element of the mapping class group $\mathcal{M}_{g}$ of genus $g$ ($\geq 2$) such that $\Phi$ is the isotopy class of a pseudo periodic map of negative twists. It is expected that, for each $\Phi$ which commutes with a hyperelliptic involution, there exists a hyperelliptic family whose monodromy is the conjugacy class of $\Phi$ in the mapping class group. In this paper, we give a partial solution for the conjecture in the case where $\Phi$ is a semistable element.

Article information

Source
Osaka J. Math., Volume 43, Number 1 (2006), 103-119.

Dates
First available in Project Euclid: 28 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1146242996

Mathematical Reviews number (MathSciNet)
MR2222403

Zentralblatt MATH identifier
1102.14007

Subjects
Primary: 14D06: Fibrations, degenerations
Secondary: 14H45: Special curves and curves of low genus 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 57M99: None of the above, but in this section 30F99: None of the above, but in this section

Citation

Ishizaka, Mizuho. Realization of hyperelliptic families with the hyperelliptic semistable monodromies. Osaka J. Math. 43 (2006), no. 1, 103--119. https://projecteuclid.org/euclid.ojm/1146242996


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References

  • E. Horikawa: On deformations of quintic surfaces, Invent. Math. 31 (1975), 43--85.
  • W.B.R. Lickorish: A finite set of generators for the homeotopy group of a $2$-manifold, Proc. Camb. Phil. Soc. 60 (1964), 769--778.
  • Y. Matsumoto and J.M. Montesinos-Amilibia: Pseudo-periodic maps and degeneration of\kern1pt Riemann surfaces I, II, Preprints, Univ. of Tokyo and Univ. Complutense de Madrid, (1991/1992).