Base loci of linear systems and the Waring problem

Mella, Massimiliano

doi:10.1090/S0002-9939-08-09545-2

Base loci of linear systems and the Waring problem
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Proc. Amer. Math. Soc. 137 (2009), 91-98 Request permission

Abstract:

The Waring problem for homogeneous forms asks for additive decompositions of a homogeneous form $f$ into powers of linear forms. A classical problem is to determine when such a decomposition is unique. In this paper I refine my earlier work (Trans. Amer. Math. Soc. 358 (2006), 5523–5538) 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 $\mathbb {P}^n$ with assigned singularities.

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