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First steps in tropical geometry

2003/06/25 by Jürgen Richter-Gebert, Bernd Sturmfels, Richter-Gebert, Jürgen +3 · 1 citation
Computer Science · Mathematics · #14A25 #15A03 #16Y60 #52B70 #68W30 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #math.AG #math.CO #msc:14A25 #msc:15A03 #msc:16Y60 #msc:52B70 #msc:68W30

paper · pdf · doi:10.48550/arxiv.math/0306366

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

openalex publication_date 2003/06/25 · arxiv created 2003/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tropical algebraic geometry is the geometry of the tropical semiring (ℝ,min,+). 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.

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