# 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} }

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

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