An algorithm for lifting points in a tropical variety
An algorithm for lifting points in a tropical variety
复制标题
热带品种提升点的算法
DOI：
10.1007/bf03191365
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发表时间：
2007
影响因子：
1.1
通讯作者：
Thomas Markwig
中科院分区：
文献类型：
--
作者：
A. Jensen;H. 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” 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 (Kn+1, 0).
