Holomorphic Lagrangian fibrations of toric hyperkahler manifolds

2011/10/03 by Craig van Coevering, Wei Zhang, van Coevering, Craig +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1110.0269

Abstract

For the sake of hyperkähler SYZ conjecture, finding holomorphic Lagrangian fibrations becomes an important issue. Toric hyperkähler manifolds are real dimension 4n non-compact hyperkähler manifolds which are quaternion analog of toric varieties. The n dimensional residue circle action on it admitting a hyperkähler moment map. We use the complex part of this moment map to construct a holomorphic Lagrangian fibration with generic fiber diffeomorphic to (ℂ^*)ⁿ, and study the singular fibers.

Citations

• The Self-Duality Equations on a Riemann Surface
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Related

• Kähler metrics and toric Lagrangian fibrations
• The dual Lagrangian fibration of known hyper-Kähler manifolds
• Sections of Lagrangian fibrations on holomorphic symplectic manifolds
• Shafarevich-Tate groups of holomorphic Lagrangian fibrations II
• Lagrangian fibrations