Incidences between points and curves
= Incidences between points and curves
{title2=$I(P,\mathcal C)=|\{(p,\gamma):p\in\gamma\}|$}
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.