Resumen de An algorithm for lifting points in a tropical variety

Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig

• 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¿ using Singular and Gfan if the base field isQ. As a byproduct we get an algorithm to compute the Puiseux expansion of a space curve singularity in (Kn+1, 0).