Upper bounds on Betti numbers of tropical prevarieties

Dima Grigoriev, Nicolai Vorobjov

Research output: Contribution to journalArticle

2 Citations (Scopus)
11 Downloads (Pure)

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 languageEnglish
Pages (from-to)127-136
Number of pages10
JournalArnold Mathematical Journal
Volume4
Issue number1
DOIs
Publication statusPublished - 1 Apr 2018

Fingerprint

Betti numbers
Upper bound
Minkowski Sum
Polynomial
Polytopes

Keywords

  • Betti numbers
  • Polyhedral complex
  • Tropical prevariety

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Upper bounds on Betti numbers of tropical prevarieties. / Grigoriev, Dima; Vorobjov, Nicolai.

In: Arnold Mathematical Journal, Vol. 4, No. 1, 01.04.2018, p. 127-136.

Research output: Contribution to journalArticle

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