强幂零特殊多重旗标的权重
Weights of strongly nilpotent special multi-flags
AI总结：
研究齐次情形下特殊多重旗标的强幂零性，通过奇点类型确定坐标权重来证明不同奇点类的多重旗标强幂零芽两两不等价，还给出古尔萨情形切向几何类权重公式，讨论相关性质并提出猜想。
AI中文摘要：
本文致力于研究两类特殊分布：特殊多重旗标及其低秩对应物古尔萨分布。已知这两类分布是弱幂零的，但仅在特殊点是强幂零的。它们的局部分类问题仍未解决，最近莫穆尔构造了特殊多重旗标的奇点类。本文研究齐次情形下的特殊多重旗标，其也是强幂零的。主要贡献是表明不同奇点类的多重旗标的强幂零芽因奇点类型唯一确定坐标权重而两两不等价。在古尔萨情形下，给出了切向几何类权重的显式公式。最后讨论了特殊多重旗标中的强幂零性质并提出了开放猜想。
英文摘要：
This paper is devoted to two distinguished families of distributions: special multi-flags and their lower-rank counterparts, Goursat distributions. It is known that these two families are weakly nilpotent but strongly nilpotent only at special points. Local classification of these objects is still open and only recently singularity classes of special multi-flags were constructed by Mormul. In this paper, we study special multi-flags in the homogeneous case, which is also strongly nilpotent. The main contribution of the present work is to show that the strongly nilpotent germs of multiflags from different singularity classes are pairwise inequivalent as the singularity type uniquely determines the weights of coordinates. In the Goursat case, explicit formulas for weights of tangential geometric classes are presented. Finally, we discuss the property of strong nilpotency among special multi-flags and state open conjectures.
