Secant varieties of toric varieties

David Cox; Jessica Sidman

doi:10.1016/j.jpaa.2006.07.008

Secant varieties of toric varieties

Algebraic Geometry 2012-01-25 v4

Authors: David Cox , Jessica Sidman

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Abstract

Let $X_P$ be a smooth projective toric variety of dimension $n$ embedded in $\PP^r$ using all of the lattice points of the polytope $P$ . We compute the dimension and degree of the secant variety $\Sec X_P$ . We also give explicit formulas in dimensions 2 and 3 and obtain partial results for the projective varieties $X_A$ embedded using a set of lattice points $A \subset P\cap\ZZ^n$ containing the vertices of $P$ and their nearest neighbors.

Keywords

toric varieties projective varieties

Cite

@article{arxiv.math/0502344,
  title  = {Secant varieties of toric varieties},
  author = {David Cox and Jessica Sidman},
  journal= {arXiv preprint arXiv:math/0502344},
  year   = {2012}
}

Comments

v1, AMS LaTex, 5 figures, 25 pages; v2, reference added; v3, This is a major rewrite. We have strengthened our main results to include a classification of smooth lattice polytopes P such that Sec X_P does not have the expected dimension. (See Theorems 1.4 and 1.5.) There was also a considerable amount of reorganization, and some expository material was eliminated; v4, 28 pages, minor corrections, additional and updated references

Secant varieties of toric varieties

Abstract

Keywords

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