Finiteness of Lagrangian fibrations with fixed invariants

Ljudmila Kamenova

doi:10.1016/j.crma.2015.12.019

Algebraic geometry

Finiteness of Lagrangian fibrations with fixed invariants

Presented by: Claire Voisin

Ljudmila Kamenova ¹

¹ Department of mathematics, 3-115, Stony Brook University, Stony Brook, NY 11794-3651, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 707-711.

Abstract
Résumé

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.

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.

Received: 2015-10-23
Accepted: 2015-12-22
Published online: 2016-05-13

DOI: 10.1016/j.crma.2015.12.019

Author's affiliations:

Ljudmila Kamenova ¹

¹ Department of mathematics, 3-115, Stony Brook University, Stony Brook, NY 11794-3651, USA

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     title = {Finiteness of {Lagrangian} fibrations with fixed invariants},
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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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