Strength and slice rank of forms are generically equal

Abstract

We prove that strength and slice rank of homogeneous polynomials of degree $d\ge 5$ over an algebraically closed field of characteristic zero coincide generically. To show this, we establish a conjecture of Catalisano, Geramita, Gimigliano, Harbourne, Migliore, Nagel and Shin concerning dimensions of secant varieties of the varieties of reducible homogeneous polynomials. These statements were already known in degrees $2\le d\le 7$ and $d=9$.

9 pages