An algorithm for lifting points in a tropical variety
Algebraic Geometry
2009-07-28 v2 Commutative Algebra
Abstract
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 Puiseux-valued ``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'' using Singular and Gfan if the base field are the rational numbers. As a byproduct we get an algorithm to compute the Puiseux expansion of a space curve singularity in (K^{n+1},0).
Cite
@article{arxiv.0705.2441,
title = {An algorithm for lifting points in a tropical variety},
author = {Anders Nedergaard Jensen and Hannah Markwig and Thomas Markwig},
journal= {arXiv preprint arXiv:0705.2441},
year = {2009}
}