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## Annales Polonici Mathematici

2013 | 108 | 3 | 219-224
Tytuł artykułu

### Unique decomposition for a polynomial of low rank

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EN
Let F be a homogeneous polynomial of degree d in m + 1 variables defined over an algebraically closed field of characteristic 0 and suppose that F belongs to the sth secant variety of the d-uple Veronese embedding of $ℙ^m$ into $ℙ^{{m+d \atop d}-1}$ but that its minimal decomposition as a sum of dth powers of linear forms requires more than s summands. We show that if s ≤ d then F can be uniquely written as $F = M₁^d + ⋯ + M_t^d + Q$, where $M₁,. .., M_t$ are linear forms with t ≤ (d-1)/2, and Q is a binary form such that $Q = ∑_{i=1}^q l_i^{d-d_i} m_i$ with $l_i$'s linear forms and $m_i$'s forms of degree $d_i$ such that $∑(d_i + 1) = s - t.$
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Tom
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219-224
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wydano
2013
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autor
• Department of Mathematics, University of Trento, 38123 Povo (TN), Italy
autor
• Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy
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