On the ideals of Secant Varieties to certain rational varieties

2006/09/02 by M. V. Catalisano, Maria Virginia Catalisano, A. V. Geramita +6
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Tensor decomposition and applications #math.AC #math.AG #msc:14M12 #msc:14M99

paper · pdf · doi:10.48550/arxiv.math/0609054

17 pages, minor changes for section 3 and references

arxiv created 2006/09/06 · arxiv updated 2009/12/01

Abstract

If \X ⊂ ¶ⁿ is a reduced and irreducible projective variety, it is interesting to find the equations describing the (higher) secant varieties of \X. In this paper we find those equations in the following cases: \X = ¶^n₁×...׶^n_t׶ⁿ is the Segre embedding of the product and n is "large" with respect to the n_i (Theorem 2.4); \X is a Segre-Veronese embedding of some products with 2 or three factors; \X is a Del Pezzo surface.

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• Singularities and syzygies of secant varieties of smooth projective varieties
• Secant varieties of Segre-Veronese embeddings of (P¹)^r
• Equations for the third secant variety of the Segre product of n projective spaces