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Taylorian points of an algebraic curve and bivariate Hermite interpolation

Len Bos, Jean-Paul Calvi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We introduce and study the notion of Taylorian points of algebraic curves in 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.

The degree of the secant variety and the join of monomial curves.

Kristian Ranestad (2006)

Collectanea Mathematica

A monomial curve is a curve parametrized by monomials. The degree of the secant variety of a monomial curve is given in terms of the sequence of exponents of the monomials defining the curve. Likewise, the degree of the join of two monomial curves is given in terms of the two sequences of exponents.

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