Open Access
January, 2011 Tropical plane geometric constructions: a transfer technique in Tropical Geometry
Luis Felipe Tabera
Rev. Mat. Iberoamericana 27(1): 181-232 (January, 2011).


The notion of geometric construction is introduced. This notion allows to compare incidence configurations both lying in the algebraic and the tropical plane. We provide sufficient conditions in a geometric construction to ensure that there is always an algebraic counterpart related by tropicalization. We also present some results to detect if this algebraic counterpart cannot exist. With these tools, geometric constructions are applied to transfer classical theorems to the tropical framework, we provide a notion of "constructible incidence theorem" and then several tropical versions of classical theorems are proved such as the converse of Pascal's, Fano's or Cayley-Bacharach theorems.


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Luis Felipe Tabera . "Tropical plane geometric constructions: a transfer technique in Tropical Geometry." Rev. Mat. Iberoamericana 27 (1) 181 - 232, January, 2011.


Published: January, 2011
First available in Project Euclid: 4 February 2011

zbMATH: 1223.14072
MathSciNet: MR2815735

Primary: 14H99
Secondary: 12J25 , 16Y60 , 51E30

Keywords: geometric constructions , incidence configurations , Tropical geometry

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 1 • January, 2011
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