Computing Tropical Varieties
代数几何
2009-12-16 v1 组合数学
摘要
The tropical variety of a -dimensional prime ideal in a polynomial ring with complex coefficients is a pure -dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing the tropical variety, and we discuss our implementation of these tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have a finite tropical basis, and a sharp lower bound is given for the size of a tropical basis for an ideal of linear forms.
引用
@article{arxiv.math/0507563,
title = {Computing Tropical Varieties},
author = {Tristram Bogart and Anders Jensen and David Speyer and Bernd Sturmfels and Rekha Thomas},
journal= {arXiv preprint arXiv:math/0507563},
year = {2009}
}
备注
22 pages, 2 figures