On rank in algebraic closure

Amichai Lampert, Tamar Ziegler

Let $\mathbf{k}$ be a field and $Q\in \mathbf{k}[x_1,\dots ,x_s]$ a form (homogeneous polynomial) of degree $d>1.$ The $\mathbf{k}$-Schmidt rank $r{k}_{\mathbf{k}}(Q)$ of $Q$ i…