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 | References | Similar Articles | Additional Information

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:
http://dx.doi.org/10.1090/S0002-9939-08-09545-2

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.