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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 5, Pages 53–74 (Mi izv8088)  

This article is cited in 1 scientific paper (total in 1 paper)

Action of the complex Monge–Ampère operator on piecewise-linear functions and exponential tropical varieties

B. Ya. Kazarnovskii

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: We consider exponential tropical varieties, which appear as analogues of algebraic tropical varieties when we pass from algebraic varieties to varieties given by zero sets of systems of exponential sums. We describe a construction of exponential tropical varieties arising from the action of the complex Monge–Ampère operator on piecewise-linear functions and show that every such variety can be obtained in this way. As an application, we deduce a criterion for the vanishing of the value of the mixed Monge–Ampère operator. This is an analogue and generalization of the criterion for the vanishing of the mixed volume of convex bodies.

Keywords: piecewise-linear function, Monge–Ampère operator, exponential tropical variety.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-8462.2012.1


DOI: https://doi.org/10.4213/im8088

Full text: PDF file (585 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:5, 902–921

Bibliographic databases:

UDC: 512.7+514.172.4
MSC: 14M25, 32W20, 52A39, 52B70
Received: 04.01.2013
Revised: 21.10.2013

Citation: B. Ya. Kazarnovskii, “Action of the complex Monge–Ampère operator on piecewise-linear functions and exponential tropical varieties”, Izv. RAN. Ser. Mat., 78:5 (2014), 53–74; Izv. Math., 78:5 (2014), 902–921

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. Ya. Kazarnovskii, “On the product of cocycles in a polyhedral complex”, Izv. Math., 81:2 (2017), 329–358  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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