Characteristic foliation on the discriminantal hypersurface of a holomorphic Lagrangian fibration

2007/10/12 by Jun-Muk Hwang, Keiji Oguiso, Hwang, Jun-Muk +1 · 1 citation
Mathematics · #14D06 #14J40 #32M05 #32M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0710.2376

openalex publication_date 2007/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a Kodaira-type classification of general singular fibers of a holomorphic Lagrangian fibration in Fujiki's class \mathcal C. Our approach is based on the study of the characteristic vector field of the discriminantal hypersurface, which naturally arises from the defining equation of the hypersurface via the symplectic form. As an application, we show that the characteristic foliation of the discriminantal hypersurface has algebraic leaves which are either rational curves or smooth elliptic curves.

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• Symplectic Singularities, Color Confinement, and the Quantum Dirac Sheaf

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