On deformations of Lagrangian fibrations

2009/03/12 by Daisuke Matsushita, Matsushita, Daisuke · 3 citations
Mathematics · #14D06 #14J40 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #math.DG #msc:14D06 #msc:14J40

paper · pdf · doi:10.48550/arxiv.0903.2098

openalex publication_date 2009/03/12 · arxiv created 2015/06/10 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be an irreducible symplectic manifold and Def(X) the Kuranishi space. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H of Def(X) such that the restriction family over H admits a family of Lagrangian fibrations over H.

Cited by

• The SYZ conjecture for singular moduli spaces of sheaves on K3 surfaces
• On Mori dreamness of blowups along space curves
• The monodromy of compact Lagrangian fibrations

Related

• Sections of Lagrangian fibrations on holomorphic symplectic manifolds
• Lagrangian fibrations
• Shafarevich-Tate groups of holomorphic Lagrangian fibrations
• Classification of Lagrangian fibrations
• Lagrangian fibrations for IHS fourfolds