We show that any fibration of a “special” compact Kähler manifold onto an Abelian variety has no multiple fibre in codimension one. This statement strengthens and extends previous results of Kawamata and Viehweg when . This also corrects the proof given in the present journal in 2004, which was incomplete.
On montre qu’une fibration d’une variété compacte Kählérienne sur une variété Abélienne n’a pas de fibre multiple en codimension . Ce résultat renforce et généralise des résultats précédents de Kawamata et Viehweg lorsque , et corrige la preuve incomplète donnée dans ce journal en 2004.
Revised:
Accepted:
Published online:
Keywords: Albanese map, special variety, orbifold base.
Mots-clés : Apllication d’Albanese, variété spéciale, base orbifolde.
Campana, Frédéric 1

@article{AIF_2023__73_5_1903_0, author = {Campana, Fr\'ed\'eric}, title = {Albanese map of special manifolds: a correction}, journal = {Annales de l'Institut Fourier}, pages = {1903--1908}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {5}, year = {2023}, doi = {10.5802/aif.3563}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3563/} }
TY - JOUR AU - Campana, Frédéric TI - Albanese map of special manifolds: a correction JO - Annales de l'Institut Fourier PY - 2023 SP - 1903 EP - 1908 VL - 73 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3563/ DO - 10.5802/aif.3563 LA - en ID - AIF_2023__73_5_1903_0 ER -
%0 Journal Article %A Campana, Frédéric %T Albanese map of special manifolds: a correction %J Annales de l'Institut Fourier %D 2023 %P 1903-1908 %V 73 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3563/ %R 10.5802/aif.3563 %G en %F AIF_2023__73_5_1903_0
Campana, Frédéric. Albanese map of special manifolds: a correction. Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 1903-1908. doi : 10.5802/aif.3563. https://aif.centre-mersenne.org/articles/10.5802/aif.3563/
[1] Varieties fibred over abelian varieties with fibres of log general type, Adv. Math., Volume 270 (2015), pp. 206-222 | DOI | MR | Zbl
[2] Special elliptic fibrations, The Fano Conference, Univ. Torino, Turin, 2004, pp. 223-234 | MR | Zbl
[3] Orbifolds, special varieties and classification theory, Ann. Inst. Fourier, Volume 54 (2004) no. 3, pp. 499-630 | DOI | Numdam | MR | Zbl
[4] Quelques propriétés de stabilité des variétés spéciales, Math. Z., Volume 283 (2016) no. 1-2, pp. 581-599 | DOI | MR | Zbl
[5] Kodaira dimension of algebraic fiber spaces over abelian varieties, Invent. Math., Volume 207 (2017) no. 1, pp. 345-387 | DOI | MR | Zbl
[6] Tores et variétés abéliennes complexes, Cours Spécialisés, 6, Société Mathématique de France, Paris; EDP Sciences, Les Ulis, 1999, vi+125 pages | MR | Zbl
[7] Characterization of abelian varieties, Compositio Math., Volume 43 (1981) no. 2, pp. 253-276 | Numdam | MR | Zbl
[8] Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics, 439, Springer-Verlag, Berlin-New York, 1975, xix+278 pages (Notes written in collaboration with P. Cherenack) | DOI | MR
[9] On the Iitaka Conjecture for Kähler Fibre Spaces (1919) (https://arxiv.org/abs/1907.06705)
Cited by Sources: