  In this paper we investigate discretizations of AGD flows whose projective
realizations are defined by intersecting different types of subspaces in
$\RP^m$. These maps are natural candidates to generalize the pentagram map,
itself defined as the intersection of consecutive shortest diagonals of a
convex polygon, and a completely integrable discretization of the Boussinesq
equation. We conjecture that the $k$-AGD flow in $m$ dimensions can be
discretized using one $k-1$ subspace and $k-1$ different $m-1$-dimensional
subspaces of $\RP^m$.
