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In contrast to the univariate case, interpolation with polynomials of a givenmaximal total degree is not always possible even if the number of interpolationpoints and the space dimension coincide. Due to that, numerous constructionsfor interpolation sets have been devised, the most popular ones being based onintersections of lines. In this paper, we study algebraic properties of somesuch interpolation configurations, namely the approaches by Radon-Berzolari andChung-Yao. By means of proper H-bases for the vanishing ideal of theconfiguration, we derive properties of the matrix of first syzygies of thisideal which allow us to draw conclusions on the geometry of the pointconfiguration.

Observations on interpolation by total degree polynomials in two variables