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.
Curvilinear schemes and maximum rank of forms / Ballico, E; Bernardi, Alessandra. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 72:1(2017), pp. 137-144. [10.4418/2017.72.1.10]
Curvilinear schemes and maximum rank of forms
Ballico E;Bernardi, Alessandra
2017-01-01
Abstract
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.File in questo prodotto:
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