Upper Bounds on Betti Numbers of Tropical Prevarieties

Upper Bounds on Betti Numbers of Tropical Prevarieties 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Upper Bounds on Betti Numbers of Tropical Prevarieties

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
D.O.I.
10.1007/s40598-018-0086-1
Publisher site
See Article on Publisher Site

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.

Journal

Arnold Mathematical JournalSpringer Journals

Published: Apr 3, 2018

References

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