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Configurations of an Articulated Arm and Singularities of Special Multi-Flags
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Configurations of an Articulated Arm and Singularities of Special Multi-Flags
Інший ID:
2010 Mathematics Subject Classification: 53C17; 58K99; 70B15; 70Q05; 93A30
DOI:10.3842/SIGMA.2014.059
DOI:10.3842/SIGMA.2014.059
Посилання:
Configurations of an Articulated Arm and Singularities of Special Multi-Flags / F. Pelletier, M. Slayman // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 16 назв. — англ.
Підтримка:
We would like to thank warmly the anonymous referees for the care and time they spent in the
detailed reading of dif ferent versions and for their questions, suggestions and comments that
helped us to significantly improve the initial version.
Дата:
2014
Переглядів:
499
Завантажень:
259
Анотація:
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.
