Newton polytopes and tropical geometry

被引：8

作者：

Kazarnovskii, B. Ya. ^{[1
]}

Khovanskii, A. G. ^{[2
,3
]}

Esterov, A. I. ^{[4
]}

机构：

[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

[2] Univ Moscow, Moscow, Russia

[3] Univ Toronto, Toronto, ON, Canada

[4] Natl Res Univ Higher Sch Econ, Moscow, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2021年 / 76卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

family of algebraic varieties; Newton polytope; ring of conditions; toric variety; tropical geometry; mixed volume; exponential sum; ALGEBRAIC-CURVES; VARIETIES; POLYHEDRA;

D O I：

10.1070/RM9937

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The practice of bringing together the concepts of 'Newton polytopes', 'toric varieties', 'tropical geometry', and 'Grobner 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.

引用

页码：91 / 175

页数：85

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