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” 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).

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