## Base loci of linear systems and the Waring problem

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- by Massimiliano Mella
- Proc. Amer. Math. Soc.
**137**(2009), 91-98 - DOI: https://doi.org/10.1090/S0002-9939-08-09545-2
- Published electronically: August 13, 2008
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## 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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## Bibliographic Information

**Massimiliano Mella**- Affiliation: Dipartimento di Matematica, Università di Ferrara, 44100 Ferrara, Italia
- Email: mll@unife.it
- Received by editor(s): October 24, 2007
- Received by editor(s) in revised form: January 8, 2008
- Published electronically: August 13, 2008
- Additional Notes: The author was partially supported by Progetto PRIN 2006 “Geometria sulle varietà algebriche” MUR
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 91-98 - MSC (2000): Primary 14J70; Secondary 14N05, 14E05
- DOI: https://doi.org/10.1090/S0002-9939-08-09545-2
- MathSciNet review: 2439429