First steps in tropical geometry

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Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. 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.
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

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Algebraic Geometry, Combinatorics, 14A25, 15A03, 16Y60, 52B70, 68W30

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http://salesiana.dossiersoluciones.com/handle/123456789/67881

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306366
 http://arxiv.org/abs/math/0306366

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arXiv