Comptes Rendus
no. 9
Algebraic Geometry
Abelian fibrations on S[n]
[Fibrations abéliennes sur S[n]]

Présenté par : Jean-Pierre Demailly

Baohua Fu1
1 Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, parc Valrose, 06108 Nice cedex 02, France
Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 593-596.

Soit S→ϕℙ1 une fibration elliptique sur une surface S, K3. Alors la composition S[n]→πS(n)→symnϕℙn donne une fibration abélienne sur S[n]. Soit E le diviseur exceptionel de π, alors symnφ∘π(E) est de dimension n−1. Dans cette Note, nous démontrons la réciproque.

Let S→ϕℙ1 be an elliptic fibration on a K3 surface S. Then the composition S[n]→πS(n)→symnϕℙn gives an Abelian fibration on S[n]. Let E be the exceptional divisor of π, then symnφ∘π(E) is of dimension n−1. We prove the inverse in this Note.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.09.022

Baohua Fu 1

1 Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, parc Valrose, 06108 Nice cedex 02, France 
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Baohua Fu. Abelian fibrations on S[n]. Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 593-596. doi : 10.1016/j.crma.2003.09.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.022/

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