Homogeneous Interpolation and Some Continued Fractions

Abstract

We prove: if $d/m<2280/721$, there is no curve of degree $d$ passing through $n=10$ general points with multiplicity $m$ in ${\mathbf{P}}^2$. Similar results are given for other special values of $n$. Our bounds can be naturally written as certain palindromic continued fractions.

21 pages, 5 figures