Newton polytopes and tropical geometry

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2021-01-01 DOI:10.1070/RM9937

Boris Yakovlevich Kazarnovskii, A. Khovanskii, A. Esterov

引用次数: 7

Abstract

The practice of bringing together the concepts of ‘Newton polytopes’, ‘toric varieties’, ‘tropical geometry’, and ‘Gröbner bases’ has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts. Bibliography: 68 titles.

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牛顿多面体和热带几何

将“牛顿多面体”、“环面变异”、“热带几何”和“Gröbner基”等概念结合在一起的实践，导致代数几何和凸几何之间形成了稳定和互利的联系。本调查致力于描述这些概念的相互作用和应用的数学领域的现状。参考书目:68种。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.