Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry

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The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it computes sufficient conditions to have an algebraic counterpart related by tropicalization. We also provide sufficient conditions in a geometric construction to ensure that the algebraic counterpart always exists. Geometric constructions are applied to transfer classical theorems to the tropical framework, we provide a notion of incidence theorems and prove several tropical versions of classical theorems like converse Pascal, Fano plane or Cayley-Bacharach.
46 Pages, 5 Figures V2. Major changes on the article, newer sections and results about geometric constructions and applications to prove theorems in tropical geometry

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Algebraic Geometry, 16Y60; 51A30; 12K10; 14H50

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http://salesiana.dossiersoluciones.com/handle/123456789/139674

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511713
 http://arxiv.org/abs/math/0511713

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arXiv