We use the theory of logarithmic line bundles to construct compactifications of spaces of roots of a line bundle on a family of curves, generalising work of a number of authors. This runs via a study of the torsion in the tropical and logarithmic jacobians (recently constructed by Molcho and Wise). Our moduli space carries a ‘double ramification cycle’ measuring the locus where the given root is isomorphic to the trivial bundle, and we give a tautological formula for this class in the language of piecewise polynomial functions (as recently developed by Molcho–Pandharipande–Schmitt and Holmes–Schwarz).

中文翻译：

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曲线上线束根的对数模

我们使用对数线丛理论来构造一系列曲线上线丛根空间的紧化，概括了许多作者的工作。这是通过对热带和对数雅可比矩阵（最近由 Molcho 和 Wise 构建的）中的挠率进行的研究来实现的。我们的模空间带有一个“双分支循环”，测量给定根与平凡丛同构的轨迹，并且我们用分段多项式函数的语言给出了此类的同义反复公式（由 Molcho–Pandharipande–Schmitt 最近开发）和福尔摩斯-施瓦茨）。