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In this paper we prove some upper bounds for the symmetric tensor rank of a symmetric tensor (or a homogeneous polynomial) in terms of integers associated to any zero-dimensional scheme evincing the scheme rank of the homogeneous polynomial.
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Edoardo Ballico, Multiple points, scheme rank and symmetric tensor rank. Port. Math. 70 (2013), no. 3, pp. 243–250DOI 10.4171/PM/1933