Computing Tropical Varieties Over Fields with Valuation
Computing Tropical Varieties Over Fields with Valuation
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通过评估计算田地的热带品种
DOI：
10.1007/s10208-019-09430-2
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发表时间：
2016
影响因子：
3
通讯作者：
Yue Ren
中科院分区：
文献类型：
--
作者：
Thomas Markwig;Yue Ren
We show how the tropical variety of an ideal I⊴K[x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I\unlhd K[x_1,\ldots ,x_n]$$\end{document} over a field K with non-trivial discrete valuation can always be traced back to the tropical variety of an ideal π-1I⊴R〚t〛[x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}I\unlhd R\llbracket t\rrbracket [x_1,\ldots ,x_n]$$\end{document} over some dense subring R in its ring of integers. We show that this connection is compatible with the Gröbner polyhedra covering them. Combined with previous works, we thus obtain a framework for computing tropical varieties over general fields with valuations, which relies on the existing theory of standard bases if π-1I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}I$$\end{document} is generated by elements in R[t,x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R[t,x_1,\ldots ,x_n]$$\end{document}.
We show how the tropical variety of an ideal I⊴K[x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I\unlhd K[x_1,\ldots ,x_n]$$\end{document} over a field K with non-trivial discrete valuation can always be traced back to the tropical variety of an ideal π-1I⊴R〚t〛[x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}I\unlhd R\llbracket t\rrbracket [x_1,\ldots ,x_n]$$\end{document} over some dense subring R in its ring of integers. We show that this connection is compatible with the Gröbner polyhedra covering them. Combined with previous works, we thus obtain a framework for computing tropical varieties over general fields with valuations, which relies on the existing theory of standard bases if π-1I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}I$$\end{document} is generated by elements in R[t,x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R[t,x_1,\ldots ,x_n]$$\end{document}.
DOI：
10.2139/ssrn.2643086
发表时间：
2018-10
期刊：
Microeconomics: General Equilibrium & Disequilibrium Models eJournal
影响因子：
--
作者：
E. Baldwin;P. Klemperer
通讯作者：
E. Baldwin;P. Klemperer
格罗布纳基于具有估值的油田
影响因子：
2
作者：
Chan A
通讯作者：
Chan A
如何使用修改来修复平面曲线的热带化
影响因子：
0.5
作者：
Marίa Angélica Cueto;Hannah Markwig
通讯作者：
Hannah Markwig