A general incidence bound in \(\mathbb{R}^d\) (Q2033938)

The aim of this paper is to derive a general upper bound for the number of incidences for a set of \(m\) points and a set of \(n\) irreducible varieties of dimension at most \(k\) and degree at most \(D\) in \({\mathbb R}^d\), with no \(K_{s, t}\) in the incidence graph. The main term (up to sub-polynomial factors) of the bound is \(m^{\frac{sk}{ds- d + k }+\epsilon}n^{\frac{ds-d}{ds- d + k}}\) where \(\epsilon\) is an arbitrarily small positive number.