Base loci of linear systems and the Waring problem

2007/10/31 by Massimiliano Mella, Mella, M.
Computer Science · Mathematics · #14E05 #14J70 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.0710.5876

openalex publication_date 2007/10/31 · 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 note I refine the work in arXiv:math/0406288v1 and answer this question under a divisibility assumption. To do this I translate the algebraic statement into a geometric one concerning the base loci of linear systems of Pⁿ with assigned singularities.

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