Secant varieties of toric varieties

Details Secant varieties of toric varieties Secant varieties of toric varieties

2005-02-16

arxiv.org/abs/math/0502344v4

J. Pure Appl. Algebra 209 (2007), no. 3, 651-669

Mathematics

Algebraic Geometry

v1, AMS LaTex, 5 figures, 25 pages; v2, reference added; v3, This is a major rewrite. We have strengthened our main results to

Scientific paper

10.1016/j.jpaa.2006.07.008

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.

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