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Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
-
Edoardo Ballico
and
Alessandra Bernardi
Published/Copyright:
June 5, 2013
Abstract.
If 
is a projective non-degenerate variety, the X-rank of a point 
is defined to be the minimum integer r such that P belongs to the span of r points of X. We describe the complete stratification of the fourth secant variety of any Veronese variety X via the X-rank. This result has an equivalent translation in terms either of symmetric tensors or of homogeneous polynomials. It allows to classify all the possible integers r that can occur in the minimal decomposition of a homogeneous polynomial of X-border rank 
(i.e. contained in the fourth secant variety) as a linear combination of powers of linear forms.
Received: 2011-11-30
Revised: 2013-05-24
Accepted: 2013-05-24
Published Online: 2013-06-05
Published in Print: 2013-06-01
© 2013 by Walter de Gruyter Berlin Boston
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- Masthead
- Erratum: Harmonic boundary value problems in a quarter ring domain [Adv. Pure Appl. Math. 3 (2012), 393–419]
- Dunkl kernel and Dunkl translation for a positive subsystem of orthogonal roots
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- Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
Keywords for this article
Rank of tensors;
polynomial decomposition;
secant varieties;
Veronese varieties
Articles in the same Issue
- Masthead
- Erratum: Harmonic boundary value problems in a quarter ring domain [Adv. Pure Appl. Math. 3 (2012), 393–419]
- Dunkl kernel and Dunkl translation for a positive subsystem of orthogonal roots
- On orthogonal polynomials associated with rational perturbations of linear functional
- Multiple solutions for a class of p(x)-Kirchhoff type problems with Neumann boundary conditions
- A further application of power increasing sequences
- Regularity of fractal interpolation functions via wavelet transform
- Finite groups with some weakly s-semipermutable subgroups
- Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
