[À propos des fibrés vectoriels amples sur les courbes en caractéristique positive.]
Soit E un fibré vectoriel ample sur une courbe projective et lisse définie sur un corps algébriquement clos de caractéristique positive. Nous construisons une famille de courbes dans l'espace total de E, paramétrisée par un espace affine, qui domine l'espace total de E et qui fournit une déformation de la section nulle (non réduite) du fibré E.
Let E be an ample vector bundle over a smooth projective curve defined over an algebraically closed field of positive characteristic. We construct a family of curves in the total space of E, parametrized by an affine space, that surjects onto the total space of E and give a deformation of (nonreduced) zero section of E.
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@article{CRMATH_2004__339_5_355_0,
author = {Biswas, Indranil and Parameswaran, A.J.},
title = {On the ample vector bundles over curves in positive characteristic},
journal = {Comptes Rendus. Math\'ematique},
pages = {355--358},
publisher = {Elsevier},
volume = {339},
number = {5},
year = {2004},
doi = {10.1016/j.crma.2004.07.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.07.006/}
}
TY - JOUR AU - Biswas, Indranil AU - Parameswaran, A.J. TI - On the ample vector bundles over curves in positive characteristic JO - Comptes Rendus. Mathématique PY - 2004 SP - 355 EP - 358 VL - 339 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.07.006/ DO - 10.1016/j.crma.2004.07.006 LA - en ID - CRMATH_2004__339_5_355_0 ER -
%0 Journal Article %A Biswas, Indranil %A Parameswaran, A.J. %T On the ample vector bundles over curves in positive characteristic %J Comptes Rendus. Mathématique %D 2004 %P 355-358 %V 339 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.07.006/ %R 10.1016/j.crma.2004.07.006 %G en %F CRMATH_2004__339_5_355_0
Biswas, Indranil; Parameswaran, A.J. On the ample vector bundles over curves in positive characteristic. Comptes Rendus. Mathématique, Tome 339 (2004) no. 5, pp. 355-358. doi : 10.1016/j.crma.2004.07.006. http://www.numdam.org/articles/10.1016/j.crma.2004.07.006/
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