We classify the possible closures of leaves of the isoperiodic foliation defined on the Hodge bundle over the moduli space of genus \(g\ge 2\) curves and prove that the foliation is ergodic on those sets. The results derive from the connectedness properties of the fibers of the period map defined on the Torelli cover of the moduli space. Some consequences on the topology of Hurwitz spaces of primitive branched coverings over elliptic curves are also obtained. To prove the results we develop the theory of augmented Torelli space, the branched Torelli cover of the Deligne–Mumford compactification of the moduli space of curves.

中文翻译：

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传递原理：从周期到等周期叶状结构

我们对亏格\(g\ge 2\)曲线模空间上 Hodge 束上定义的等周期叶状结构的叶子的可能闭包进行分类，并证明叶状结构在这些集合上是遍历的。结果源自在模空间的 Torelli 覆盖上定义的周期图的纤维的连通性属性。还得到了关于椭圆曲线上本原分支覆盖的 Hurwitz 空间拓扑的一些结果。为了证明结果，我们发展了增广 Torelli 空间理论，即曲线模空间的 Deligne–Mumford 紧化的分支 Torelli 覆盖。