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Line bundles on Schubert varieties. (English) Zbl 0688.14047

Vector bundles on algebraic varieties, Pap. Colloq., Bombay 1984, Stud. Math., Tata Inst. Fundam. Res. 11, 499-528 (1987).
[For the entire collection see Zbl 0653.00006.]
The aim of this paper is to fix a gap (found by V. Kac) in the proof of the main result of M. Demazure’s paper in Ann. Sci. Éc. Norm. Supér., IV. Sér. 7, 53-88 (1974; Zbl 0312.14009). In the same time the author’s methods also yield a proof of the fact that the results of Demazure even cover Spec(\({\mathbb{Z}})\) (this had been conjectured by Demazure himself in the above mentioned paper).
Reviewer: L.Bădescu

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14N10 Enumerative problems (combinatorial problems) in algebraic geometry