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arXiv · 1110.0269

Holomorphic Lagrangian fibrations of toric hyperkahler manifolds

Craig van Coevering·Wei Zhang
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Abstract

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

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Craig van Coevering, Wei Zhang. 2011-10-03. Holomorphic Lagrangian fibrations of toric hyperkahler manifolds. https://arxiv.org/abs/1110.0269

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