Grassmann secants, identifiability, and linear systems of tensors

For any irreducible non-degenerate variety X ⊂ P r , we give a criterion for the ( k , s ) -identifiability of X. If k s − 1 < r, then the ( k , s ) - identifiability holds for X if and only if the s-identifiability holds for the Segre product Seg (P k × X ) . Moreover, if the s-th secant variety of X is not defective and it does not fill the ambient space, then we can produce a family of pairs ( k , s ) for which the ( k , s ) -identifiability holds for X. © 2012 Elsevier Inc. All rights reserved.