The Monodromy of Compact Lagrangian Fibrations
Abstract
Abstract We study the monodromy representations underlying compact Lagrangian fibrations. In the case where the associated period map is generically immersive, we prove that the mondromy representation is irreducible over $\mathbb{C}$. In the alternative case where the fibration is isotrivial, we recover a result of [16], proving that its fibers are isogeneous to a power of an elliptic curve. We show that over $\mathbb{C}$, the monodromy representation underlying an isotrivial Lagrangian fibration is a direct sum of two irreducible $\mathbb{C}$-local systems.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Geometry and complex manifolds
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 7
- Publication date
- 31 March 2026
- Language
- EN