Ideals of varieties parameterized by certain symmetric tensors

Abstract

The ideal of a Segre variety is generated by the 2-minors of a generic hypermatrix of indeterminates. We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of weak generic hypermatrix which allows us to treat also the case of projection of Veronese surfaces from a set of generic points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension 2.

19 pages

References in corpus (3)

• On degeneration of tensors and algebras
• Higher secant varieties of Segre-Veronese varieties
• On the ideals and singularities of secant varieties of Segre varieties

Cited by in corpus (16)

• General Tensor Decomposition, Moment Matrices and Applications
• Four lectures on secant varieties
• Higher secant varieties of ${\mathbb{P}}^n\times {\mathbb{P}}^1$ embedded in bi-degree $(a,b)$
• Linear determinantal equations for all projective schemes
• Waring, tangential and cactus decompositions
• A note on the cactus rank for Segre-Veronese varieties
• Rank 3 Quadratic Generators of Veronese Embeddings
• Skew-Symmetric Tensor Decomposition
• On the X-rank with respect to linear projections of projective varieties
• Are all Secant Varieties of Segre Products Arithmetically Cohen-Macaulay?
• Geometric conditions for strict submultiplicativity of rank and border rank
• Minimal primes of ideals arising from conditional independence statements
• A uniqueness result on the decompositions of a bi-homogeneous polynomial
• Representation Theory of ${\mathbb{Z}}_2^{\ast n}$
• On the rank index of projective curves of almost minimal degree
• s-Hankel hypermatrices and 2 x 2 determinantal ideals