Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry

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dc.creatorTabera, Luis Felipe
dc.date2005-11-29
dc.date2007-10-10
dc.date.accessioned2026-07-07T08:35:12Z
dc.date.available2026-07-07T08:35:12Z
dc.descriptionThe 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.
dc.description46 Pages, 5 Figures V2. Major changes on the article, newer sections and results about geometric constructions and applications to prove theorems in tropical geometry
dc.identifierhttps://arxiv.org/abs/math/0511713
dc.identifierhttp://arxiv.org/abs/math/0511713
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139674
dc.subjectAlgebraic Geometry
dc.subject16Y60; 51A30; 12K10; 14H50
dc.titleTropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry
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