Tropicalizing the space of admissible covers
Tropicalizing the space of admissible covers
复制标题
热带化允许覆盖的空间
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Dhruv Ranganathan
中科院分区：
文献类型：
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作者：
R. Cavalieri;H. Markwig;Dhruv Ranganathan
研究了热带Hurwitz模空间与经典Hurwitz模空间之间的关系。在Abramovich，Caporaso和Payne最近的工作之后，我们勾画了任意亏格曲线的广义Hurwitz覆盖的模空间的热带化。我们的方法是求助于可容许覆盖的几何，它紧凑了Hurwitz方案。研究了热带容许覆盖的组合模空间与经典容许覆盖空间的Berkovich分析的骨架之间的关系。我们利用非阿基米德几何的技巧证明了热带重言式映射和经典重言式映射通过热带化是相容的，并且经典分支映射的程度可以从热带一侧恢复。作为结果，我们在模空间的水平上得到了古典的和热带的Hurwitz数相等的证明。
We study the relationship between tropical and classical Hurwitz moduli spaces. Following recent work of Abramovich, Caporaso and Payne, we outline a tropicalization for the moduli space of generalized Hurwitz covers of an arbitrary genus curve. Our approach is to appeal to the geometry of admissible covers, which compactify the Hurwitz scheme. We study the relationship between a combinatorial moduli space of tropical admissible covers and the skeleton of the Berkovich analytification of the classical space of admissible covers. We use techniques from non-archimedean geometry to show that the tropical and classical tautological maps are compatible via tropicalization, and that the degree of the classical branch map can be recovered from the tropical side. As a consequence, we obtain a proof, at the level of moduli spaces, of the equality of classical and tropical Hurwitz numbers.
曲线的热带覆盖层及其模空间
影响因子：
1.6
作者：
Arne Buchholz;Hannah Markwig
通讯作者：
Hannah Markwig