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arXiv · 1708.01029

Ranks on the boundaries of secant varieties

Edoardo Ballico
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Abstract

In many cases (e.g. for many Segre or Segre embeddings of multiprojective spaces) we prove that a hypersurface of the $b$-secant variety of $X\subset \mathbb {P}^r$ has $X$-rank $>b$. We prove it proving that the $X$-rank of a general point of the join of $b-2$ copies of $X$ and the tangential variety of $X$ is $>b$.

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Edoardo Ballico. 2017-08-03. Ranks on the boundaries of secant varieties. https://arxiv.org/abs/1708.01029

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