Minimal decomposition of binary forms with respect to tangential projections

Edoardo Ballico 1 Alessandra Bernardi 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Let $C\subset \mathbb{P}^n$ be a rational normal curve and let $\ell_O:\mathbb{P}^{n+1}\dashrightarrow \mathbb{P}^n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$. Hence $X:= \ell_O(C)\subset \mathbb{P}^n$ is a linearly normal cuspidal curve with degree $n+1$. For any $P = \ell_O(B)$, $B\in \mathbb{P}^{n+1}$, the $X$-rank $r_X(P)$ of $P$ is the minimal cardinality of a set $S\subset X$ whose linear span contains $P$. Here we describe $r_X(P)$ in terms of the schemes computing the $C$-rank or the border $C$-rank of $B$.
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https://hal.inria.fr/hal-00645983
Contributor : Alessandra Bernardi <>
Submitted on : Monday, November 28, 2011 - 11:11:36 PM
Last modification on : Thursday, January 11, 2018 - 4:02:47 PM

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  • HAL Id : hal-00645983, version 1
  • ARXIV : 1007.2822

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Edoardo Ballico, Alessandra Bernardi. Minimal decomposition of binary forms with respect to tangential projections. 2011. ⟨hal-00645983⟩

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