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Preprints, Working Papers, ... Year : 2012

Curvilinear schemes and maximum rank of forms

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.
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Dates and versions

hal-00747023 , version 1 (30-10-2012)

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Edoardo Ballico, Alessandra Bernardi. Curvilinear schemes and maximum rank of forms. 2012. ⟨hal-00747023⟩
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