Singularities of linear systems and the Waring Problem

2004/06/15 by Massimiliano Mella, Mella, Massimiliano
Computer Science · Mathematics · #14E05 #14J70 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation #Tensor decomposition and applications #math.AG #msc:14E05 #msc:14J70 #msc:14N05

paper · pdf · doi:10.48550/arxiv.math/0406288

15 pages AmsLaTeX2e

arxiv created 2004/06/15 · openalex publication_date 2004/06/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Waring problem for homogeneus 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 I answer this question when the degree of f is greater than the number of variables. To do this I translate the algebraic statement into a geometric one concerning the singularities of linear systems of Pⁿ with assigned singularities.

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