Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry
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.
Cite
@article{arxiv.math/0511713,
title = {Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry},
author = {Luis Felipe Tabera},
journal= {arXiv preprint arXiv:math/0511713},
year = {2007}
}
Comments
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