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arXiv · 2112.09324

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

Masayuki Sukenaga
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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 $\mathbb{R}_{\leq 0}^2$ 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.

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Masayuki Sukenaga. 2021-12-17. Smooth tropical complete intersection curves of genus $3$ in $\mathbb{R}^3$. https://arxiv.org/abs/2112.09324

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