Matrixwise (approach to unexpected hypersurfaces) Reloaded

Abstract

In the paper we provide a new method of proving the existence of a hypersurface of degree $d$ in ${\mathbb{P}}^n$, with a general point of multiplicity $m$ and vanishing at a given set of points $Z$, by looking at weak combinatorics of a set $Z$. This method has a direct application in the theory of unexpected hypersurfaces, where many of the examples are based only on computer experiments.