Ballico, Edoardo ; Bernardi, Alessandra
(2010)
*Minimal decomposition of binary forms with respect to tangential projections.*
[Preprint]

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## Abstract

Let $C\subset \PP n$ be a rational normal curve and let $\ell_O:\PP {n+1}\dashrightarrow \PP n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$.
In this paper we relate the minimum number $r$ of addenda that are needed to write a binary form $p$ of degree $(n+1)$ and defined over an algebraically closed field of characteristic zero as linear combination of $(n+1)$-th powers of linear binary forms $L_1, \ldots , L_r$, with the minimum number of addenda that are required to write $\ell_O(p)$ as linear combination of elements belonging to $\ell_O(C)$.

Abstract

Let $C\subset \PP n$ be a rational normal curve and let $\ell_O:\PP {n+1}\dashrightarrow \PP n$ be any tangential projection form a point $O\in T_AC$ where $A\in C$.
In this paper we relate the minimum number $r$ of addenda that are needed to write a binary form $p$ of degree $(n+1)$ and defined over an algebraically closed field of characteristic zero as linear combination of $(n+1)$-th powers of linear binary forms $L_1, \ldots , L_r$, with the minimum number of addenda that are required to write $\ell_O(p)$ as linear combination of elements belonging to $\ell_O(C)$.

Document type

Preprint

Creators

Keywords

Secant varieties, $X$-rank, Cuspidal curves, Rational normal curves, Linear projections.

Subjects

DOI

Deposit date

19 Jul 2010 10:00

Last modified

17 Feb 2016 15:09

URI

## Other metadata

Document type

Preprint

Creators

Keywords

Secant varieties, $X$-rank, Cuspidal curves, Rational normal curves, Linear projections.

Subjects

DOI

Deposit date

19 Jul 2010 10:00

Last modified

17 Feb 2016 15:09

URI

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