Finiteness of Lagrangian fibrations with fixed invariants

Ljudmila Kamenova

doi:10.1016/j.crma.2015.12.019

Finiteness of Lagrangian fibrations with fixed invariants

Ljudmila Kamenova

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	707-711
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	7
DOIs	https://doi.org/10.1016/j.crma.2015.12.019
State	Published - Jul 1 2016

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10.1016/j.crma.2015.12.019

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title = "Finiteness of Lagrangian fibrations with fixed invariants",

abstract = "We prove finiteness of the deformation classes of hyperk{\"a}hler 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 hyperk{\"a}hler Lagrangian fibrations with an ample line bundle of a given degree on the general fibre of the fibration.",

author = "Ljudmila Kamenova",

note = "Publisher Copyright: {\textcopyright} 2016 Acad{\'e}mie des sciences",

year = "2016",

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84967224377

U2 - 10.1016/j.crma.2015.12.019

DO - 10.1016/j.crma.2015.12.019

M3 - Article

AN - SCOPUS:84967224377

SN - 1631-073X

VL - 354

SP - 707

EP - 711

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7

ER -

Finiteness of Lagrangian fibrations with fixed invariants

Abstract

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