Singularities of linear systems and the Waring problem

Mella, Massimiliano

doi:10.1090/S0002-9947-06-03893-1

Singularities of linear systems and the Waring problem
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Trans. Amer. Math. Soc. 358 (2006), 5523-5538 Request permission

Abstract:

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 $\mathbb {P}^n$ with assigned singularities.

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