Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry, we describe a modular modification of the moduli space of curves over which the Abel-Jacobi map extends. We also describe the attendant deformation theory and virtual fundamental class of this moduli space. This recovers the double ramification cycle, as well as variants associated to differentials.

中文翻译：

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Abel–Jacobi部分的对数压缩

给定具有加权标记点的平滑曲线，Abel-Jacboi贴图在曲线上产生线束。该图无法扩展到稳定尖曲线的模空间的整个边界。使用对数和热带几何，我们描述了曲线的模量空间的模数修改，Abel-Jacobi映射在该模数空间上扩展。我们还描述了该模空间的伴随变形理论和虚拟基本类别。这样可以恢复双分支循环以及与差异相关的变体。