Singularities of linear systems and the Waring problem

By Massimiliano Di Mella. 2004

69 citations recorded by the source corpus.

The Waring problem for homogeneous forms asks for additive decomposition of a form f into powers of linear forms. A classical problem is to determine when such a decomposition is unique. In this paper we answer this question when the degree of f is greater than the number of variables. To do this we translate the algebraic statement into a geometric one concerning the singularities of linear systems of P" with assigned singularities.

Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6c09e83bc973e6b1ee00f76bec986cb4b74b295a

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In Algebra and Number Theory

In Computational Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On generic identifiability of symmetric tensors of subgeneric rank (2015, background): “Actually, Theorem 6.1.2 of [26] only intended to collect previous results by Ballico [4], Ciliberto and Chiantini [8], and Mella [27,28], which are individually correct.”
Tensor decompositions, alternating least squares and other tales (2009, methodology): “In the symmetric case, stronger results have been obtained recently and prove that the decomposition is essentially unique with probability 1 if the dimension does not exceed the order [42].”
On the Concept of k‐Secant Order of a Variety (2006, background): “Unfortunately little is known about this question in general (see however the recent work of Mella [14]).”
Decomposition of homogeneous polynomials with low rank (2010, unknown): “∈ Z (see [19], [17], [18], [9] also for”
Classical Algebraic Geometry: A Modern View (2012, background): “Mella [381], [382], where it is proven that there are no new cases when n = 2, d ≥ 5 and n ≥ 3 and n divides ( n+d n−1 ) .”
Equations for secant varieties of Veronese and other varieties (2011, unknown): “[10, 36, 1] The k-weakly defective varieties vd(P n) are the triples (k, d, n): (i) the k-defective varieties, namely (k, 2, n), k = 2, .”