Unique decomposition for a polynomial of low rank

• Autorzy: Edoardo Ballico , Alessandra Bernardi
• Języki publikacji: EN

Abstrakty

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 $∑(d_i + 1) = s - t.$

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 14N15: Classical problems, Schubert calculus
• 15A69: Multilinear algebra, tensor products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 108
• Numer: 3
• Strony: 219-224

Daty

wydano

2013

Twórcy

autor

Edoardo Ballico

• Department of Mathematics, University of Trento, 38123 Povo (TN), Italy

autor

Alessandra Bernardi

• Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy

Identyfikatory

DOI

10.4064/ap108-3-2