Smooth tropical complete intersection curves of genus 3 in $$\mathbb {R}^3$$ R 3

IF 0.7 2区数学 Q2 MATHEMATICS

Collectanea Mathematica Pub Date : 2022-08-27 DOI:10.1007/s13348-022-00372-7

Masayuki Sukenaga

引用次数: 1

Abstract

We develop a method for describing the tropical complete intersection of a tropical hypersurface and a tropical plane in $\mathbb {R}^3$. This involves a method for determining the topological type of the intersection of a tropical plane curve and $\mathbb {R}_{\le 0}^2$ by using a polyhedral complex. As an application, we study smooth tropical complete intersection curves of genus 3 in $\mathbb {R}^3$. In particular, we show that there are no smooth tropical complete intersection curves in $\mathbb {R}^3$ whose skeletons are the lollipop graph of genus 3. This gives a partial answer to a problem of Morrison in [6].

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在$$\mathbb {R}^3$$ R 3中属3的光滑热带完全相交曲线

本文在$\mathbb {R}^3$中提出了一种描述热带超曲面与热带平面的热带完全相交的方法。这涉及到使用多面体复合体确定热带平面曲线与$\mathbb {R}_{\le 0}^2$相交的拓扑类型的方法。作为应用，我们研究了$\mathbb {R}^3$中3属的光滑热带完全相交曲线。特别地，我们证明了$\mathbb {R}^3$中不存在光滑的热带完全相交曲线，其骨架是3属的棒棒糖图。这部分回答了Morrison在[6]中的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Collectanea Mathematica 数学-数学

CiteScore

2.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.