An algorithm for lifting points in a tropical variety

Autores: Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 2, 2008, págs. 129-165
Idioma: inglés
DOI: 10.1007/bf03191365
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Resumen
- 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).