Singularity classes of special multi-flags, I

The construction of the geometric singularity classes of special multi-flags was exhaustively done in [P. Mormul, SIGMA, 5:Paper 102, 22 pages, 2009] for special 2-flags, i.e. when flag's width, typically denoted by m, was 2. Now analogous singularity classes are being constructed for special flags of all widths m≥2, compatible with and extending by far the construction in the mentioned paper.