Tensor ranks on tangent developable of Segre varieties

TL;DR

This paper characterizes tensor ranks on tangent developables of Segre varieties, providing algorithms for rank computation, and proves Comon's conjecture for tensors in tangential Veronese varieties.

Contribution

It introduces a stratification of tensor ranks on tangent developables, offers algorithms for tensor decomposition, and proves a significant conjecture in tensor theory.

Findings

Stratification of tensor rank on tangent developables

Algorithms for tensor rank computation and decomposition

Proof of Comon's conjecture for tangential Veronese tensors

Abstract

We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon's conjecture on the rank of symmetric tensors for those tensors belonging to tangential varieties to Veronese varieties.