Newton polytopes and tropical geometry

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.