In this paper we consider a generic degree $d$ form $ F $ in $n+1$ variables.
In particular, we investigate the existence of star configurations apolar to
$F$, that is the existence of apolar sets of points obtained by the $ n $-wise
intersection of $ r $ general hyperplanes of $ \mathbb{P}^n $. We present a
complete answer for all values of $(d,r,n)$ except for $(d,d+1,2)$ when we
present an algorithmic approach

Carlini, Enrico