Border Waring Rank via Asymptotic Rank
arXiv:1907.03487
Abstract
We investigate an extension of a lower bound on the Waring (cactus) rank of homogeneous forms due to Ranestad and Schreyer. We show that for particular classes of homogeneous forms, for which a generalization of this method applies, the lower bound extends to the level of border (cactus) rank. The approach is based on recent results on tensor asymptotic rank.
arXiv comment12 pages; Comments are welcome
References in corpus (9)
- Hilbert schemes of 8 points
- Tensor rank is not multiplicative under the tensor product
- The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
- On the cactus rank of cubics forms
- Geometric lower bounds for generalized ranks
- Four lectures on secant varieties
- On the partially symmetric rank of tensor products of W-states and other symmetric tensors
- Border rank is not multiplicative under the tensor product
- Border Ranks of Monomials