On maximal curves of $n$-correct sets

Suppose $\mathcal{X}$ is an $n$-correct set of nodes in the plane, that is, it admits a unisolvent interpolation with bivariate polynomials of total degree less than or equal to $n\mathrm{.}$ Then an algebraic curve $q$ of degree $k\le n$ can pass through at most $d(n,k)$ nodes of $\text{Xset},$ where $d(n,k)=\left(\genfrac{}{}{0px}{}{n+2}{2}\right)-\left(\genfrac{}{}{0px}{}{n+2-k}{2}\right)\mathrm{.}$ A curve $q$ of degree $k\le n$ is called maximal if it passes through exactly $d(n,k)$ nodes of $\mathcal{X}\mathrm{.}$ In particular, a maximal line is a line passing through $d(n,1)=n+1$ nodes of $\mathcal{X}\mathrm{.}$ Maximal curves are an important tool for the study of $n$-correct sets. We present new properties of maximal curves, as well as extensions of known properties.