  In this article we study forbidden loci and typical ranks of forms with
respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line
bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to
supports of non-reduced apolar schemes. We show that, in those cases, this is
contained in the forbidden locus. Furthermore, for these embeddings, we give a
component of the real rank boundary, the hypersurface dividing the minimal
typical rank from higher ones. These results generalize to a class of
embeddings of $\mathbb P^n\times \mathbb P^1$. Finally, in connection with real
rank boundaries, we give a new interpretation of the $2\times n \times n$
hyperdeterminant.
