# Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications

@article{Basu2018MultidegreeBO,
title={Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications},
author={S. Basu and Anthony Rizzie},
journal={Discrete \& Computational Geometry},
year={2018},
volume={59},
pages={553-620}
}
• Published 14 July 2015
• Mathematics, Computer Science
• Discrete & Computational Geometry
We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that have a more refined dependence on the degrees of the polynomials defining them than results known before. Our method also unifies several different types of results under a single framework, such as bounds depending on the total degrees, on multi-degrees, as well as in the case of quadratic and partially quadratic polynomials. The bounds we present in the case of partially quadratic polynomials offer a… Expand
6 Citations

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