realizationMatroids.lib — a Singular library for relative realizability questions on tropical curves. In tropical geometry, one question to ask is the following: given a one-dimensional balanced polyhedral fan C which is set theoretically contained in the tropicalization trop(Y) of an algebraic variety Y in K^n, where K is any algebraically closed field, does there exist a curve X in Y such that trop(X) = C? This equality of C and trop(X) denotes an equality of both, the fans trop(X) and C and their multiplicities on the maximal cones. The relative realization space of C with respect to Y is the space of all algebraic curves in Y which tropicalize to C. This library provides procedures deciding relative realizability for tropical fan curves, i.e. one-dimensional balanced polyhedral fans, contained in two-dimensional matroidal fans trop(Y) where Y is a projective plane in K^n. Here K is any algebraically closed field.

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  1. Birkmeyer, Anna Lena; Gathmann, Andreas; Schmitz, Kirsten: The realizability of curves in a tropical plane (2017)