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Base loci of linear systems and the Waring problem
Author(s):
Massimiliano
Mella
Journal:
Proc. Amer. Math. Soc.
137
(2009),
91-98.
MSC (2000):
Primary 14J70;
Secondary 14N05, 14E05
Posted:
August 13, 2008
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Abstract:
The Waring problem for homogeneous forms asks for additive decompositions of a homogeneous form  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  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:
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
Posted:
August 13, 2008
Additional Notes:
The author was partially supported by Progetto PRIN 2006 ``Geometria sulle varietà algebriche'' MUR
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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