Ausgezeichnete Basen von Milnorgittern einfacher Singularitäten (Q1065081)

The main goal of this paper is to discuss a certain set of ordered bases of the Milnor lattice of a simple singularity which I call distinguished [up to the ordering they correspond to the ''weakly distinguished'' bases of \textit{S. M. Husein-Zade} ; cf. Russ. Math. Surv. 32, No.2, 23-69 (1977); translation from Usp. Mat. Nauk 32, No.2(194), 23-65 (1977; Zbl 0363.32010)], by means of the corresponding root system \((=set\) of vanishing cycles). It is shown that every ordered basis of the Milnor lattice, which consists of vanishing cycles (i.e. of roots), is distinguished. At the same time I prove a conjecture of Husein-Zade (in the case of a simple singularity) concerning the orbits of the braid- group on these bases. The orbits are explicitly determined.