[Finitude des fibrations lagrangiennes à invariants fixes]
Nous démontrons la finitude des classes de déformation des fibrations lagrangiennes hyperkählériennes, de dimension quelconque, avec constante de Fujiki et discriminant du réseau de Beauville–Bogomolov–Fujiki fixes. Nous montrons également qu'il n'y a qu'un nombre fini de classes de déformation des fibrations lagrangiennes hyperkählériennes avec un fibré en droite ample de degré donné sur la fibre générale de la fibration.
We prove finiteness of the deformation classes of hyperkähler Lagrangian fibrations in any fixed dimension with fixed Fujiki constant and discriminant of the Beauville–Bogomolov–Fujiki lattice. We also prove there are only finitely many deformation classes of hyperkähler Lagrangian fibrations with an ample line bundle of a given degree on the general fibre of the fibration.
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@article{CRMATH_2016__354_7_707_0,
author = {Ljudmila Kamenova},
title = {Finiteness of {Lagrangian} fibrations with fixed invariants},
journal = {Comptes Rendus. Math\'ematique},
pages = {707--711},
publisher = {Elsevier},
volume = {354},
number = {7},
year = {2016},
doi = {10.1016/j.crma.2015.12.019},
language = {en},
}
Ljudmila Kamenova. Finiteness of Lagrangian fibrations with fixed invariants. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 707-711. doi : 10.1016/j.crma.2015.12.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.019/
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