Ranks on the boundaries of secant varieties

Edoardo Ballico

Ranks on the boundaries of secant varieties

Algebraic Geometry 2017-08-04 v1

Authors: Edoardo Ballico

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 $>b$ .

Keywords

secant varieties X-rank Segre embeddings multiprojective spaces tangential variety join of varieties

Cite

@article{arxiv.1708.01029,
  title  = {Ranks on the boundaries of secant varieties},
  author = {Edoardo Ballico},
  journal= {arXiv preprint arXiv:1708.01029},
  year   = {2017}
}

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