Singularities of linear systems and the Waring Problem

Details Singularities of linear systems and the Waring Problem Singularities of linear systems and the Waring Problem

2004-06-15

arxiv.org/abs/math/0406288v1

Mathematics

Algebraic Geometry

15 pages AmsLaTeX2e

Scientific paper

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 $P^n$ with assigned singularities.

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