On $D$-invariant points and local Taylor interpolation on algebraic hypersurfaces in $\mathbb R^N$

Abstract

We give the definition of $D$-invariant points on an irreducible algebraic hypersurface $V$ in $\mathbb R^N$. We show that every regular point on irreducible quadratic hypersurface in $\mathbb R^N$ is $D$-invariant. We prove that the local Taylor interpolation projector at a regular point $\mathbf a\in V$ is an ideal projector if and only if $\mathbf a$ is $D$-invariant.