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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Base loci of linear systems and the Waring problem


Author: Massimiliano Mella
Journal: Proc. Amer. Math. Soc. 137 (2009), 91-98
MSC (2000): Primary 14J70; Secondary 14N05, 14E05
Published electronically: August 13, 2008
MathSciNet review: 2439429
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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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Additional Information

Massimiliano Mella
Affiliation: Dipartimento di Matematica, Università di Ferrara, 44100 Ferrara, Italia
Email: mll@unife.it

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09545-2
PII: S 0002-9939(08)09545-2
Keywords: Waring, linear system, singularities, birational maps
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.