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Russian Mathematical Surveys, 2021, Volume 76, Issue 1, Pages 91–175
DOI: https://doi.org/10.1070/RM9937 (Mi rm9937) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Newton polytopes and tropical geometry

B. Ya. Kazarnovskiia, A. G. Khovanskiibc, A. I. Esterovd

a Institute for Information Transmission Problems of the Russian Academy of Sciences
b Independent University of Moscow
c University of Toronto, Toronto, Canada
d National Research University Higher School of Economics
English version PDF (1131 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM9937
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.
Keywords: family of algebraic varieties, Newton polytope, ring of conditions, toric variety, tropical geometry, mixed volume, exponential sum.
Funding agency Grant number
Canadian Grant 156833-17
Russian Foundation for Basic Research 20-01-00579
The second author was supported by Canadian grant no. 156833-17. The third author was supported by the Russian Foundation for Basic Research (grant no. 20-01-00579).
Received: 25.11.2019
Russian version:
Uspekhi Matematicheskikh Nauk, 2021, Volume 76, Issue 1(457), Pages 95–190
DOI: https://doi.org/10.4213/rm9937
Bibliographic databases:
Document Type: Article
UDC: 512.7+514.17
MSC: Primary 14M15, 14Txx; Secondary 14C17
Language: English
Original paper language: Russian
Citation: B. Ya. Kazarnovskii, A. G. Khovanskii, A. I. Esterov, “Newton polytopes and tropical geometry”, Uspekhi Mat. Nauk, 76:1(457) (2021), 95–190; Russian Math. Surveys, 76:1 (2021), 91–175
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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    		Успехи математических наук Russian Mathematical Surveys
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    References:69
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