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Singularities of linear systems and the Waring problem

Author(s): Massimiliano Mella
Journal: Trans. Amer. Math. Soc. 358 (2006), 5523-5538.
MSC (2000): Primary 14J70; Secondary 14N05, 14E05
Posted: July 21, 2006
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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.

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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

DOI: 10.1090/S0002-9947-06-03893-1
PII: S 0002-9947(06)03893-1
Keywords: Waring, linear system, singularities, birational maps
Received by editor(s): June 17, 2004
Received by editor(s) in revised form: November 17, 2004
Posted: July 21, 2006
Additional Notes: This work was partially supported by Progetto Cofin 2002 ``Geometria sulle varietà algebriche'' Miur, Eager
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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