arXiv subjects

Masayuki Sukenaga

Publications and source records attributed to Masayuki Sukenaga.

3 recordsLinked to original sources

arXiv2024

Minimum volumes of tropical rational functions

When a tropical rational function φon R^n is given, we can represent it as φ=f-g with tropical polynomials f and g. We develop the duality theorem for tropical rational functions to define the volume of the pair (f, g). We show that when n=1, we can find a representation of φ(x) \neq -\infty as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) \oplus (yg(x)) is unique up to translation, but when n=2 this is not true.

math.AG↗

arXiv2022

Tropical lifting problem for the intersection of plane curves

Given a tropical divisor $D$ in the intersection of two tropical plane curves, we study when it can be realized as the tropicalization of the intersection of two algebraic curves, and give a sufficient condition. We show that under a certain condition involving a graph determined by these tropical curves, we can algorithmically find algebraic curves such that the tropicalization of their intersection is $D$.

math.AG↗

arXiv2022

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

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.

math.AG↗