The tropicalization of the moduli space of curves
The tropicalization of the moduli space of curves
复制标题
曲线模空间的热带化
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Payne
中科院分区：
文献类型：
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作者：
D. Abramovich;L. Caporaso;S. Payne
我们表明，骨架的Deligne-Mumford-Knudsen模量堆栈的稳定曲线的模空间的扩展热带曲线自然识别，这是兼容的“天真”集理论的热带化地图。证明通过一般的结构结果的骨架上的环形Deligne-Mumford堆栈。此外，我们构造重言遗忘，抓持，和胶合模空间之间的扩展热带曲线的映射，并表明它们是兼容的代数设置类似的重言映射。
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.