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arXiv · 1104.3648

On the rank of a symmetric form

Kristian Ranestad·Frank-Olaf Schreyer
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Abstract

We give a lower bound for the degree of a finite apolar subscheme of a symmetric form F, in terms of the degrees of the generators of the annihilator ideal of F. In the special case, when F is a monomial x_0^d_0 x_2^d_2... x_n^d_n with d_0<= d_1<=...<=d_n-1<= d_n we deduce that the minimal length of an apolar subscheme of F is (d_0+1)...(d_n-1+1), and if d_0=..=d_n, then this minimal length coincides with the rank of F.

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Kristian Ranestad, Frank-Olaf Schreyer. 2011-04-19. On the rank of a symmetric form. https://arxiv.org/abs/1104.3648

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