First steps in tropical geometry
Algebraic Geometry
2007-05-23 v2 Combinatorics
Abstract
Tropical algebraic geometry is the geometry of the tropical semiring . Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on plane curves and linear spaces. New results include a complete description of the families of quadrics through four points in the tropical projective plane and a counterexample to the incidence version of Pappus' Theorem.
Cite
@article{arxiv.math/0306366,
title = {First steps in tropical geometry},
author = {Jürgen Richter-Gebert and Bernd Sturmfels and Thorsten Theobald},
journal= {arXiv preprint arXiv:math/0306366},
year = {2007}
}
Comments
Revised version based on reviewers' comments; also corrected the statement of Theorem 2.6. To appear in Proc. Conference on Idempotent Mathematics and Mathematical Physics, Vienna 2003 (G.L. Litvinov and V.P. Maslov, eds.), Contemporary Mathematics, AMS. 29 pages, many figures