%0 Journal Article
%T An algorithm for lifting points in a tropical variety
%A Anders Nedergaard Jensen
%A Hannah Markwig
%A Thomas Markwig
%J Mathematics
%D 2007
%I arXiv
%X 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).
%U http://arxiv.org/abs/0705.2441v2