 Incidences between points and curves

For finite sets of points $P$ and geometric curves $\mathcal{C}$, a point-curve incidence is a pair $(p,\gamma )$ with $p\in \gamma$. The incidence count is $I(P,\mathcal{C})={\sum }_{\gamma \in \mathcal{C}}|P\cap \gamma |$. Bounds in incidence geometry exploit restrictions on how curves can meet points, rather than treating the incidence relation as an arbitrary bipartite graph.