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arXiv · 1709.08594

Upper bounds on Betti numbers of tropical prevarieties

Dima Grigoriev·Nicolai Vorobjov
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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.

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Dima Grigoriev, Nicolai Vorobjov. 2017-09-25. Upper bounds on Betti numbers of tropical prevarieties. https://arxiv.org/abs/1709.08594

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