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Stratification of the fourth secant variety of Veronese varieties via the symmetric rank

Stratification of the fourth secant variety of Veronese varieties via the symmetric rank 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter
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