Linear Pencils of Tropical Plane Curves.

Linear pencils of tropical plane curves are parameterized by tropical lines (i.e. trees) in the space of coefficients. We study pencils of tropical curves with n-element support that pass through n−2 general points in the plane. Richter-Gebert et al. proved that such trees are compatible with their support set, and they conjectured that every compatible tree can be realized by a point configuration. In this article, we prove this conjecture. Our approach is based on a characterization of the fixed loci of tropical linear pencils. [ABSTRACT FROM AUTHOR]