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Expected term bases for generic multivariate Hermite interpolation

Marcin Dumnicki
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Abstract

The main goal of the paper is to find an effective estimation for the minimal number of generic points in $\mathbb K^2$ for which the basis for Hermite interpolation consists of the first $\ell$ terms (with respect to total degree ordering). As a result we prove that the space of plane curves of degree $d$ having generic singularities of multiplicity $\leq m$ has the expected dimension if the number of low order singularities (of multiplicity $k\leq12$) is greater then some $r(m,k)$. Additionally, the upper bounds for $r(m,k)$ are given.

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Marcin Dumnicki. 2005-03-30. Expected term bases for generic multivariate Hermite interpolation. https://arxiv.org/abs/math/0503701

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