Portal de Periódicos da CAPES

An algorithm for lifting points in a tropical variety

2008; Springer Science+Business Media; Volume: 59; Issue: 2 Linguagem: Inglês

10.1007/bf03191365

2038-4815

Anders Jensen, Hannah Markwig, Thomas Markwig,

Algebraic Geometry and Number Theory

The aim of this paper is to give a constructive proof of one of the basic theorems of tropical geometry: given a point on a tropical variety (defined using initial ideals), there exists a Puiseuxvalued "lift" of this point in the algebraic variety. This theorem is so fundamental because it justifies why a tropical variety (defined combinatorially using initial ideals) carries information about algebraic varieties: it is the image of an algebraic variety over the Puiseux series under the valuation map. We have implemented the "lifting algorithm" usingSingular and Gfan if the base field is ℚ. As a byproduct we get an algorithm to compute the Puiseux expansion of a space curve singularity in (K n+1, 0).