Comptes Rendus
no. 5
Algebraic Geometry
On the ample vector bundles over curves in positive characteristic
[À propos des fibrés vectoriels amples sur les courbes en caractéristique positive.]

Présenté par : Christophe Soulé

Indranil Biswas1 ; A.J. Parameswaran1
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 355-358.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.07.006
Indranil Biswas 1 ; A.J. Parameswaran 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 
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     pages = {355--358},
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Indranil Biswas; A.J. Parameswaran. On the ample vector bundles over curves in positive characteristic. Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 355-358. doi : 10.1016/j.crma.2004.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.006/

[1] D. Barlet; T. Peternell; M. Schneider On two conjectures of Hartshorne's, Math. Ann., Volume 286 (1990), pp. 13-25

[2] R. Hartshorne Ample Subvarieties of Algebraic Varieties, Lecture Notes in Math., vol. 156, Springer-Verlag, Berlin, 1970

[3] A. Langer Semistable sheaves in positive characteristic, Ann. Math., Volume 159 (2004), pp. 251-276

[4] S. Ramanan; A. Ramanathan Some remarks on the instability flag, Tôhoku Math. J., Volume 36 (1984), pp. 269-291

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