%0 Journal Article
%T Curvilinear schemes and maximum rank of forms
%A Edoardo Ballico
%A Alessandra Bernardi
%J Mathematics
%D 2012
%I arXiv
%X We define the \emph{curvilinear rank} of a degree $d$ form $P$ in $n+1$ variables as the minimum length of a curvilinear scheme, contained in the $d$-th Veronese embedding of $\mathbb{P}^n$, whose span contains the projective class of $P$. Then, we give a bound for rank of any homogenous polynomial, in dependance on its curvilinear rank.
%U http://arxiv.org/abs/1210.8171v2