标题： 紧致拉格朗日纤维化的单值化 显示英文标题

标题： The monodromy of compact Lagrangian fibrations

摘要： 我们研究了紧拉格朗日纤维化背后的单值表示。 在伴随周期映射通常是浸入的情形下，我们证明单值表示在\(\mathbb{C}\)上是不可约的。 在纤维化是等变的另一种情形下，我们重新得到了\cite{kim-laza-martin23}的结果，证明其纤维同源于一个椭圆曲线的幂。 我们证明，在\(\mathbb{C}\)上，等变拉格朗日纤维化的单值表示是两个不可约\(\mathbb{C}\)局部系统的直和。 显示英文摘要

摘要： 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 \cite{kim-laza-martin23}, 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.