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Published online by Cambridge University Press: 17 March 2022
In this chapter, we study general incidence bounds in R^d. As a warm-up, we first derive an incidence bound for curves in R^3. The main result of this chapter is a general point-variety incidence bound in R^d. This result relies on another polynomial partitioning theorem, for the case where the points are on a constant-degree variety. The proof of this partitioning theorem relies on Hilbert polynomials. In particular, we use Hilbert polynomials to derive a polynomial ham sandwich theorem for points on a variety.
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