Configurations of an Articulated Arm and Singularities of Special Multi-Flags

[摘要] P. Mormul has classified the singularities of special multi-flags in terms of “EKR class'' encoded by sequences $j_1,\dots, j_k$ of integers (see [Singularity Theory Seminar, Warsaw University of Technology, Vol. 8, 2003, 87-100] and [ Banach Center Publ. , Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]). However, A.L. Castro and R. Montgomery have proposed in [ Israel J. Math. 192 (2012), 381-427] a codification of singularities of multi-flags by RC and RVT codes. The main results of this paper describe a decomposition of each ''EKR'' set of depth $1$ in terms of RVT codes as well as characterize such a set in terms of configurations of an articulated arm. Indeed, an analogue description for some ''EKR'' sets of depth $2$ is provided. All these results give rise to a complete characterization of all ''EKR'' sets for $1\leq k\leq 4$.

[关键词] special multi-flags distributions;Cartan prolongation;spherical prolongation;articulated arm;rigid bar