Upper bounds on Betti numbers of tropical prevarieties

Dima Grigoriev; Nicolai Vorobjov

doi:10.1007/s40598-018-0086-1

Upper bounds on Betti numbers of tropical prevarieties

Dima Grigoriev, Nicolai Vorobjov

Université de Lille

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2 Citations (SciVal)

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Abstract

We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, via the maximal degree of these polynomials. In sparse setting, the bound involves the number of the monomials.

Original language	English
Pages (from-to)	127-136
Number of pages	10
Journal	Arnold Mathematical Journal
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s40598-018-0086-1
Publication status	Published - 1 Apr 2018

Keywords

Betti numbers
Polyhedral complex
Tropical prevariety

ASJC Scopus subject areas

General Mathematics

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10.1007/s40598-018-0086-1

TropBettiArnold030818
The final publication is available at Springer via https://doi.org/10.1007/s40598-018-0086-1.
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KW - Polyhedral complex

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Upper bounds on Betti numbers of tropical prevarieties

Abstract

Keywords

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