realizationMatroids swMATH ID: 19075 Software Authors: Birkmeyer, A.L.; Anna Lena Winstel Description: 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. Homepage: http://www.mathematik.uni-kl.de/agag/mitglieder/professoren/gathmann/software/realize/ Dependencies: Singular Related Software: SINGULAR Cited in: 1 Document Cited by 3 Authors 1 Birkmeyer, Anna Lena 1 Gathmann, Andreas 1 Schmitz, Kirsten Cited in 1 Serial 1 Discrete & Computational Geometry Cited in 1 Field 1 Algebraic geometry (14-XX) Citations by Year