标题： 曲线模空间的热带化 显示英文标题

标题： The tropicalization of the moduli space of curves

摘要： 我们证明了稳定曲线的Deligne-Mumford-Knudsen模堆栈的骨架可以自然地与扩展热带曲线的模空间相识别，并且这与“直接”的集合论热带化映射相容。 证明过程涉及对环柄Deligne-Mumford堆栈骨架的一般结构结果。 此外，我们构建了扩展热带曲线模空间之间的典型遗忘、粘合和粘接映射，并证明它们与代数设定中的类似典型映射相容。 显示英文摘要

摘要： We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, clutching, and gluing maps between moduli spaces of extended tropical curves and show that they are compatible with the analogous tautological maps in the algebraic setting.