A note on the cactus rank for Segre-Veronese varieties

TL;DR

This paper provides an upper bound for the cactus rank of multi-homogeneous polynomials, advancing understanding of tensor decompositions in algebraic geometry.

Contribution

It introduces a new upper bound for the cactus rank applicable to all multi-homogeneous polynomials, extending previous results.

Findings

Established a universal upper bound for cactus rank

Applied the bound to Segre-Veronese varieties

Enhanced understanding of polynomial tensor decompositions

Abstract

We give an upper bound for the cactus rank of any multi-homogeneous polynomial.