Curves with only triple ramification

Stefan Schröer[1]

  • [1] Universität Bayreuth, Mathematische Institut, 95440 Bayreuth (Allemagne)

Annales de l'Institut Fourier (2003)

  • Volume: 53, Issue: 7, page 2225-2241
  • ISSN: 0373-0956

Abstract

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We show that the set of smooth curves of genus g ≥ 0 admitting a branched covering X → ℙ 1 with only triple ramification points is of dimension at least max ( 2 g - 3 , g ) . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.

How to cite

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Schröer, Stefan. "Curves with only triple ramification." Annales de l'Institut Fourier 53.7 (2003): 2225-2241. <http://eudml.org/doc/116097>.

@article{Schröer2003,
abstract = {We show that the set of smooth curves of genus $g\ge 0$ admitting a branched covering $X\rightarrow \{\mathbb \{P\}\}^1$ with only triple ramification points is of dimension at least $\max (2g-3,g)$. In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.},
affiliation = {Universität Bayreuth, Mathematische Institut, 95440 Bayreuth (Allemagne)},
author = {Schröer, Stefan},
journal = {Annales de l'Institut Fourier},
keywords = {triple ramification; tame coverings; Belyi's Theorem; smooth curves; ramification points; families; moduli space of curves},
language = {eng},
number = {7},
pages = {2225-2241},
publisher = {Association des Annales de l'Institut Fourier},
title = {Curves with only triple ramification},
url = {http://eudml.org/doc/116097},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Schröer, Stefan
TI - Curves with only triple ramification
JO - Annales de l'Institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 7
SP - 2225
EP - 2241
AB - We show that the set of smooth curves of genus $g\ge 0$ admitting a branched covering $X\rightarrow {\mathbb {P}}^1$ with only triple ramification points is of dimension at least $\max (2g-3,g)$. In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.
LA - eng
KW - triple ramification; tame coverings; Belyi's Theorem; smooth curves; ramification points; families; moduli space of curves
UR - http://eudml.org/doc/116097
ER -

References

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  12. H. Laufer, Taut two-dimensional singularities, Math. Ann 205 (1973), 131-164 Zbl0281.32010MR333238
  13. F. Orgogozo, I. Vidal, Le théorème de spécialisation du groupe fondamental, Courbes semi-stables et groupe fondamental en géométrie algébrique 187 (2000), 169-184, Birkhäuser, Basel Zbl0978.14033
  14. M. Saïdi, Revêtements modérés et groupe fondamental de graphe de groupes, Compositio Math. 107 (1997), 319-338 Zbl0929.14016MR1458754
  15. S. Schröer, The strong Franchetta Conjecture in arbitrary characteristics Zbl1059.14058MR1984659
  16. J.-P. Serre, Groupes algébriques et corps de classes, 1264 (1975), Hermann, Paris Zbl0318.14004MR466151
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