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.
@article{1296828832,
author = {Tabera
,
Luis Felipe},
title = {Tropical plane geometric constructions: a transfer technique in Tropical Geometry},
journal = {Rev. Mat. Iberoamericana},
volume = {27},
number = {1},
year = {2011},
pages = { 181-232},
language = {en},
url = {http://dml.mathdoc.fr/item/1296828832}
}
Tabera
,
Luis Felipe. Tropical plane geometric constructions: a transfer technique in Tropical Geometry. Rev. Mat. Iberoamericana, Tome 27 (2011) no. 1, pp. 181-232. http://gdmltest.u-ga.fr/item/1296828832/