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On refined count of rational tropical curves
Pure and Applied Mathematics Quarterly ( IF 0.7 ) Pub Date : 2020-01-01 , DOI: 10.4310/pamq.2020.v16.n4.a5
Eugenii Shustin 1
Affiliation  

We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts plane rational tropical curves with an unmarked vertex of arbitrary valency. It was motivated by the tropical enumeration of plane cuspidal tropical curves given by Y. Ganor and the author, which naturally led to consideration of plane tropical curves with an unmarked four-valent vertex. Another refined invariant counts rational tropical curves of a given degree in the Euclidean space of arbitrary dimension matching specific constraints, which make the spacial refined invariant similar to known planar invariants.

中文翻译:

有理热带曲线的细化计算

我们解决了细化(即,取决于形式参数)热带枚举不变量的存在问题,并且我们提出了两个有理标记热带曲线的细化计数的新示例。新的不变量之一计算具有任意价数的未标记顶点的平面有理热带曲线。它的动机是由 Y. Ganor 和作者给出的平面尖顶热带曲线的热带枚举,这自然导致考虑具有未标记的四价顶点的平面热带曲线。另一个细化的不变量计算任意维数匹配特定约束的欧几里得空间中给定度数的有理热带曲线,这使得空间细化的不变量类似于已知的平面不变量。
更新日期:2020-01-01
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