## Singularities of linear systems and the Waring problem

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## 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.## References

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## Additional Information

**Massimiliano Mella**- Affiliation: Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy
- Email: mll@unife.it
- Received by editor(s): June 17, 2004
- Received by editor(s) in revised form: November 17, 2004
- Published electronically: July 21, 2006
- Additional Notes: This work was partially supported by Progetto Cofin 2002 “Geometria sulle varietà algebriche” Miur, Eager
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**358**(2006), 5523-5538 - MSC (2000): Primary 14J70; Secondary 14N05, 14E05
- DOI: https://doi.org/10.1090/S0002-9947-06-03893-1
- MathSciNet review: 2238925