Abelian fibrations on S[n]

Baohua Fu

doi:10.1016/j.crma.2003.09.022

Algebraic Geometry

Abelian fibrations on S^[n]

Presented by: Jean-Pierre Demailly

Baohua Fu ¹

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.

Abstract
Résumé

Let $S \overset{ϕ}{\to} ℙ^{1}$ be an elliptic fibration on a K3 surface S. Then the composition $S^{[n]} \overset{π}{\to} S^{(n)} \overset{{sym}^{n} ϕ}{\to} ℙ^{n}$ 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.

Soit $S \overset{ϕ}{\to} ℙ^{1}$ une fibration elliptique sur une surface S, K3. Alors la composition $S^{[n]} \overset{π}{\to} S^{(n)} \overset{{sym}^{n} ϕ}{\to} ℙ^{n}$ 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.

Received: 2003-06-05
Accepted: 2003-09-15
Published online: 2003-10-27

DOI: 10.1016/j.crma.2003.09.022

Author's affiliations:

Baohua Fu ¹

¹ Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, parc Valrose, 06108 Nice cedex 02, France

@article{CRMATH_2003__337_9_593_0,
     author = {Baohua Fu},
     title = {Abelian fibrations on {\protect\emph{S}\protect\textsuperscript{[\protect\emph{n}]}}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {593--596},
     publisher = {Elsevier},
     volume = {337},
     number = {9},
     year = {2003},
     doi = {10.1016/j.crma.2003.09.022},
     language = {en},
}

TY  - JOUR
AU  - Baohua Fu
TI  - Abelian fibrations on S[n]
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 593
EP  - 596
VL  - 337
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2003.09.022
LA  - en
ID  - CRMATH_2003__337_9_593_0
ER  -

%0 Journal Article
%A Baohua Fu
%T Abelian fibrations on S[n]
%J Comptes Rendus. Mathématique
%D 2003
%P 593-596
%V 337
%N 9
%I Elsevier
%R 10.1016/j.crma.2003.09.022
%G en
%F CRMATH_2003__337_9_593_0

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/

References
Cited by

[1] A. Beauville Variétés dont la première classe de Chern est nulle, J. Differential Geom., Volume 18 (1983), pp. 755-782

[2] B. Hassett; Y. Tschinkel Rational curves on holomorphic symplectic fourfolds, Geom. Funct. Anal., Volume 11 (2001) no. 6, pp. 1201-1228

[3] J.-M. Hwang; N. Mok Projective manifolds dominated by Abelian varieties, Math. Z., Volume 238 (2001), pp. 89-100

[4] D.G. Markushevich Integrable symplectic structures on compact complex manifolds, Math. USSR-Sb., Volume 59 (1988) no. 2, pp. 459-469

[5] D. Matsushita On fibre space structures of a projective irreducible symplectic manifold, Topology, Volume 38 (1999) no. 1, pp. 79-83

[6] D. Mumford Abelian Varieties. With Appendices by C.P. Ramanujam and Yuri Manin, Reprint. Stud. Math., 5, Tata Institute of Fundamental Research, Bombay, 1985 (Oxford etc.: Oxford University Press)

[7] J. Sawon Abelian fibred holomorphic symplectic manifolds, Turkish J. Math., Volume 27 (2003) no. 1, pp. 197-230

Cited by Sources:

Comments - Policy