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# Curvilinear schemes and maximum rank of forms

2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
Document type :
Preprints, Working Papers, ...

Cited literature [14 references]

https://hal.inria.fr/hal-00747023
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Tuesday, October 30, 2012 - 1:06:10 PM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
Long-term archiving on: : Thursday, January 31, 2013 - 3:46:33 AM

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### Identifiers

• HAL Id : hal-00747023, version 1
• ARXIV : 1210.8171

### Citation

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

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