Linear pencils of tropical plane curves

TL;DR

This paper studies linear pencils of tropical plane curves, characterizing their fixed loci and showing that compatible pencils originate from general point configurations, advancing the understanding of tropical algebraic geometry.

Contribution

It provides a characterization of fixed points in tropical linear pencils and proves that compatible pencils are derived from general configurations.

Findings

Characterization of points in the fixed locus of tropical linear pencils

Proof that compatible linear pencils originate from general configurations

Extension of classical algebraic geometry concepts to tropical setting

Abstract

Analogously as in classical algebraic geometry, linear pencils of tropical plane curves are parameterized by tropical lines in a coefficient space. A special example of such a linear pencil is the set of tropical plane curves with an n-element support set through a general configuration of n points in the tropical plane. In [RGST], it is proved that these linear pencils are compatible with their support set. In this article, we give a characterization of points lying in the fixed locus of a tropical linear pencil and show that each compatible linear pencil comes from a general configuration.