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

Abstract

P. Mormul has classified the singularities of special multi-flags in terms of “EKR class'' encoded by sequences j1,…,jk 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≤k≤4.