摘要翻译：
本文用纯组合方法研究热带曲线上因子的线性等价类的结构和算法性质。特别地，给出了热带曲线的Riemann-Roch定理的一个初等证明，类似于Baker和Norine最近对图的Riemann-Roch定理的证明。此外，还证实了Baker关于非度量图上除数D的秩等于相应度量图上除数D的秩的猜想，并构造了计算热带曲线上除数秩的算法。
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英文标题：
《Rank of divisors on tropical curves》
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作者：
Jan Hladk\'y, Daniel Kr\'al', Serguei Norine
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最新提交年份：
2016
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分类信息：

一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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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：
  We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the Riemann-Roch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph is confirmed, and an algorithm for computing the rank of a divisor on a tropical curve is constructed.
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PDF链接：
https://arxiv.org/pdf/0709.4485