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Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry

Luis Felipe Tabera
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Abstract

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.

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BibTeXRIS

Luis Felipe Tabera. 2007-10-10. Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry. https://arxiv.org/abs/math/0511713

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