On Maximal Curves of n-Correct Sets

Suppose 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 $$n.$$ Then an algebraic curve q of degree k≤ n can pass through at most d(n,k):=n+22-n+2-k2 nodes of X. A curve q of degree k≤ n is called maximal if it passes through exactly $$d(n,k)$$ nodes of X. In particular, a maximal line is a line passing through $$d(n,1)=n+1$$ nodes of X. 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.