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摘要翻译：
在热带几何学中，给定一条曲面变体中的曲线，定义一个嵌入欧几里得空间中的对应图。我们研究了亏格为零和亏格为一的曲线的这一过程的反转问题。我们的方法侧重于通过参数化来描述曲线，而不是通过定义方程来描述曲线；给出了有理函数在亏格为零的情况下的参数化，非阿基米德椭圆函数在亏格为一的情况下的参数化。对于亏零曲线，可以用完全组合的方式刻画那些可以提升的图。对于亏一曲线，证明了Mikhalkin给出的某些条件是充分的，并给出了一个新的必要条件。
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英文标题：
《Uniformizing Tropical Curves I: Genus Zero and One》
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作者：
David E Speyer
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In tropical geometry, given a curve in a toric variety, one defines a corresponding graph embedded in Euclidean space. We study the problem of reversing this process for curves of genus zero and one. Our methods focus on describing curves by parameterizations, not by their defining equations; we give parameterizations by rational functions in the genus zero case and by non-archimedean elliptic functions in the genus one case. For genus zero curves, those graphs which can be lifted can be characterized in a completely combinatorial manner. For genus one curves, show that certain conditions identified by Mikhalkin are sufficient and we also identify a new necessary condition.
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PDF链接：
https://arxiv.org/pdf/0711.2677
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