On Certain Loci of Hankel $r$-Planes of $\mathbb P^m$

We study the loci of Hankel $(l+1)$-planes in $\mathbb P^m$ containing a fixed $l$-plane $\pi_l$. We investigate the singular locus of the variety $H(r,m)$ of Hankel $r$-planes in $\mathbb P^m$.