Taylorian points of an algebraic curve and bivariate Hermite interpolation

Bos, Len; Calvi, Jean-Paul

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 545-577.

We introduce and study the notion of Taylorian points of algebraic curves in ${ℂ}^2$, which enables us to define intrinsic Taylor interpolation polynomials 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.

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