Relative disposition of the Schubert supervarieties and resolution of their singularities (Q1105656)

This note is an announcement of two results on Schubert supervarieties and is a continuation of the previous work by the author and \textit{Yu. I. Manin} [Funkt. Anal. Appl. 18, 329-330 (1984); translation from Funkts. Anal. Prilozh. 18, No.4, 75-76 (1984; Zbl 0608.14038)]. The first result is a combinatorial description of the ordering in the Weyl supergroup defined by the position of the Schubert subvarieties corresponding to the elements of the Weyl supergroups of the complex algebraic supergroups SL(m\(| n)\), OSp(m\(| n)\) (automorphisms of an even symmetric form), Sp(m) (automorphisms of odd skew form), Q(m) (automorphisms of an odd involution). In the latter ordering \(w_ 1<w_ 2\) iff \(X_{w_ 1}\subset \bar X_{w_ 2}.\) The second result is a superanalog of Demazure's resolution of the Schubert varieties using Bott-Samelson schemes [\textit{M. Demazure}, Ann. Sci. Éc. Norm. Supér., IV. Sér. 7, 53-88 (1974; Zbl 0312.14009)]. This brief note contains definitions and statements of the results.