Taylorian points of an algebraic curve and bivariate Hermite interpolation

Abstract

We introduce and study the notion of Taylorian points of algebraic curves in C 2 , which enables us to define intrinsic Taylor interpolation polyno- mials on curves. These polynomials in turn lead to the construction of a well- behaved Hermitian scheme on curves, of which we give several examples. We show that such Hermitian schemes can be collected to obtain Hermitian bivariate polynomial interpolation schemes.