Torsor Neron models of hyperkahler manifolds

2025/09/15 by Kamenova, Ljudmila, Verbitsky, Misha · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.12369

Abstract

Let M be a compact hyperkahler manifold equipped with a Lagrangian fibration π: M → X, and M' the smooth locus of π. We prove that over a complement to a codimension ≥ 2 subset in X, the projection π: M' → X has a natural structure of a torsor over an abelian group bundle, which can be understood as a complex analytic variant of the Néron model construction. This gives an independent proof of a result by Y.-J. Kim.

Citations

• Néron models, minimal models, and birational group actions
• The Néron model of a higher-dimensional Lagrangian fibration
• Shafarevich-Tate groups of holomorphic Lagrangian fibrations
• Lagrangian fibrations
• Motivic zeta functions of degenerating Calabi-Yau varieties
• Abelian Calabi-Yau threefolds: Néron models and rational points

Cited by

• Minimal multiplicity of fiber components in abelian fibrations

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• The Néron model of a higher-dimensional Lagrangian fibration
• A variant of Neron models over curves
• On torsors under elliptic curves and Serre's pro-algebraic structures
• Weierstrass models
• A generalization of the Neron models of Green, Griffiths and Kerr