Polynomial foldings and rank of tensors

Steven P. Diaz, Adam Lutoborski

Abstract: We review facts about rank, multilinear rank, multiplex rank and generic rank of tensors as well as folding of a tensor into a matrix of multihomogeneous polynomials. We define the new concept of folding rank of tensors and compare its properties to other ranks. We review the concept of determinantal schemes associated to a tensor. Then we define the new concept of a folding generic tensor meaning that all its determinantal schemes behave generically. Our main theorem states that for "small" 3-tensors, any folding generic tensor has generic rank, and the reverse does not always hold.

Journal: Journal of Commutative Algebra, 8(2), 2016, 173-206.

DOI: 10.1216/JCA-2016-8-2-173