Tropical geometry of moduli spaces of weighted stable curves
Tropical geometry of moduli spaces of weighted stable curves
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加权稳定曲线模空间的热带几何
DOI：
10.1112/jlms/jdv032
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Martin Ulirsch
中科院分区：
文献类型：
--
作者：
Martin Ulirsch
哈塞特的加权稳定曲线模空间形成了具有标记点的平滑曲线模空间的一类重要的交替模紧化。在本文中，我们定义了这些模空间的热带模拟，并表明朴素集合论热带化图可以通过非阿基米德骨架上的自然变形收缩来识别。这一结果概括了阿布拉莫维奇、卡波拉索和佩恩处理带标记点的平滑曲线模空间的 Deligne-Knudsen-Mumford 紧化的工作。我们还研究同义反复映射的热带类比，研究热带模空间对权重数据的依赖性，并考虑 Losev-Manin 空间的示例。
Hassett's moduli spaces of weighted stable curves form an important class of alternate modular compactifications of the moduli space of smooth curves with marked points. In this article, we define a tropical analog of these moduli spaces, and show that the naive set‐theoretic tropicalization map can be identified with a natural deformation retraction onto the non‐Archimedean skeleton. This result generalizes work of Abramovich, Caporaso, and Payne treating the Deligne–Knudsen–Mumford compactification of the moduli space of smooth curves with marked points. We also study tropical analogs of the tautological maps, investigate the dependence of the tropical moduli spaces on the weight data, and consider the example of Losev–Manin spaces.