Curves of genus \(g\) which admit a map to \(\mathbf {P}^{1}\) with specified ramification profile \(\mu\) over \(0\in \mathbf {P}^{1}\) and \(\nu\) over \(\infty\in \mathbf {P}^{1}\) define a double ramification cycle \(\mathsf{DR}_{g}(\mu,\nu)\) on the moduli space of curves. The study of the restrictions of these cycles to the moduli of nonsingular curves is a classical topic. In 2003, Hain calculated the cycles for curves of compact type. We study here double ramification cycles on the moduli space of Deligne-Mumford stable curves.

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曲线的模空间上的双分支循环

属\（g \）的曲线，其允许映射到\（\ mathbf {P} ^ {1} \）且具有指定的分支轮廓\（\ mu \）到\（0 \ in \ mathbf {P} ^ {1 } \）和\（\ infty \ in \ mathbf {P} ^ {1} \）上的\（\ nu \）定义了一个双分支周期\（\ mathsf {DR} _ {g}（\ mu，\ nu ）\）在曲线的模空间上。研究这些循环对非奇异曲线模量的限制是一个经典的课题。Hain在2003年计算了紧凑型曲线的循环。我们在这里研究Deligne-Mumford稳定曲线的模空间上的双分支循环。