Tropical ideals with Hilbert function two
Magdalena Anna Zajaczkowska · Warwick Research Archive Portal (University of Warwick) · 2018
We study tropical ideals with Hilbert function two, i.e., homogeneous ideals in the tropical polynomial semiring such that each degree has the underlying structure of a valuated matroid of rank two. We classify all such ideals when the matroid is over the field ꓐ. We discuss the realizability of such ideals when they are in two and three variables. We also give necessary conditions for a sequence of valuated matroids over R to correspond to a tropical ideal in two variables