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arXiv · 2504.21740

The monodromy of compact Lagrangian fibrations

Edward Varvak
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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 Kim--Laza--Martin, 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.

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Edward Varvak. 2025-04-30. The monodromy of compact Lagrangian fibrations. https://doi.org/10.1093/imrn%2Frnag057

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