Nous étudions la théorie des déformations des revêtements galoisiens sauvagement ramifiés entre courbes stables. On examine d’abord les problèmes locaux, point double formel avec pour groupe d’inertie un -groupe, puis le cas global. On compare enfin les obstructions globales au relèvement aux obstructions locales.
In this paper we study deformation theory of wildly ramified Galois coverings between stables curves. We first study the local aspects concerning a formal double point with a -group as inertia group, and then the global case. We compare global obstructions and local obstructions to the lifting problem.
Classification : 14H10, 14H30, 14B10
Mots clés : revêtement, déformation, point double
@article{AIF_2005__55_6_1905_0,
author = {Bertin, Jos\'e and Maugeais, Sylvain},
title = {D\'eformations \'equivariantes des courbes semistables},
journal = {Annales de l'Institut Fourier},
pages = {1905--1941},
publisher = {Association des Annales de l'institut Fourier},
volume = {55},
number = {6},
year = {2005},
doi = {10.5802/aif.2146},
zbl = {1095.14022},
mrnumber = {2187940},
language = {fr},
url = {www.numdam.org/item/AIF_2005__55_6_1905_0/}
}
Bertin, José; Maugeais, Sylvain. Déformations équivariantes des courbes semistables. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 1905-1941. doi : 10.5802/aif.2146. http://www.numdam.org/item/AIF_2005__55_6_1905_0/
[Ab] Raynaud's group-scheme and reduction of coverings (preprint, arXiv math.AG/0304352, http://arxiv.org/abs/math.AG/0304352)
[BM2] Déformations formelles de revêtements : un principe local-global (to appear Israel math. journal) | Zbl 1133.14011
[BM] Déformations formelles des revêtements sauvagement ramifiés, Inv. Math., Volume 141 (2000) no. 1, pp. 195-238 | MR 1767273 | Zbl 0993.14014
[BR] Champs de Hurwitz (2005) (Prépublication Institut Fourier)
[CK] Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic, Duke Math J., Volume 116 (2003) no. 3, pp. 431-470 | Article | MR 1958094 | Zbl 01941437
[DM] The irreducibilty of the space of curves of a given genus, Inst. Hautes Études Sci. Publ. Math., Volume 36 (1969), pp. 75-109 | Article | Numdam | MR 262240 | Zbl 0181.48803
[Ek] Boundary behaviour of Hurwitz schemes in The moduli space of curves (Texel Island, 1994), Progr. Math., Volume 129 (1995), pp. 173-198 | MR 1363057 | Zbl 0862.14018
[Gr] Sur quelques points d'algèbre homologique, Tôhoku Math. J., Volume 9 (1957) no. 2, pp. 119-221 | Article | MR 102537 | Zbl 0118.26104
[HM] On the Kodaira dimension of the moduli space of curves, Invent. Math., Volume 67 (1982), pp. 23-86 | Article | MR 664324 | Zbl 0506.14016
[Ja] Torsion free sheaves and the moduli space of higher spin curves, Compositio. Math., Volume 110 (1998) no. 3, pp. 291-333 | Article | MR 1602060 | Zbl 0912.14010
[Ma] Relèvement des revêtements -cycliques des courbes rationnelles semi-stables, Math. Ann., Volume 327 (2003), pp. 365-393 | Article | MR 2015076 | Zbl 02018276
[Ma2] Déformations équivariantes des courbes stables (2003) (Thèse de l'Université de Bordeaux)
[OP] Gromov-Witten theory, Hurwitz numbers, and Matrix models I (preprint arXiv:math.AG/0101147, http://arxiv.org/abs/math.AG/0101147)
[Pr] Deformation of Wildly ramified Actions on Curves (preprint arXiv: math.AG/0403056, http://arxiv.org/abs/math.AG/0403056)
[Se] Corps locaux, Hermann | Zbl 0137.02601
[Wa] Equisingular deformation of plane algebroid curves, Trans. Amer. Math. Soc., Volume 193 (1974), pp. 143-170 | Article | MR 419439 | Zbl 0294.14007
[We2] Deformation of tame admissible covers of curves (Lecture notes Ser.) Volume 256 (1999) | Zbl 0995.14008
[We] Formal deformation of curves with group scheme action (2003) (preprint arXiv:math.AG/0212145, http://arxiv.org/abs/math.AG/0212145)
