Upper bounds on Betti numbers of tropical prevarieties
Algebraic Geometry
2018-03-13 v2
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.
Keywords
Cite
@article{arxiv.1709.08594,
title = {Upper bounds on Betti numbers of tropical prevarieties},
author = {Dima Grigoriev and Nicolai Vorobjov},
journal= {arXiv preprint arXiv:1709.08594},
year = {2018}
}
Comments
9 pages. Upper bounds are slightly improved