Geometry on Grassmannians and applications to splitting bundles and smoothing cycles. (English) Zbl 0208.48501


14M15 Grassmannians, Schubert varieties, flag manifolds
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
57R20 Characteristic classes and numbers in differential topology
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[1] M. F. Atiyah, Vector bundles over an elliptic curve,Proc. Lond. Math. Soc. (3), vol. 7 (1957), 414–452. · Zbl 0084.17305 · doi:10.1112/plms/s3-7.1.414
[2] A. Grothendieck, La théorie des classes de Chern,Bull. Soc. math. France, vol. 86 (1958), 137–154. · Zbl 0091.33201
[3] A. Grothendieck, Fibrés vectoriels, fibrés projectifs, fibrés en drapeaux, exposé 12,in fascicule I ofSéminaire H. Cartan, 13 (1960–1961).
[4] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I and II,Ann. of Math., vol. 79 (1964), 109–326. · Zbl 0122.38603 · doi:10.2307/1970486
[5] H. Hironaka, Smoothing of algebraic cycles of small dimensions,Amer. Journ. of Math., vol. 90 (1968), 1–54. · Zbl 0173.22801 · doi:10.2307/2373425
[6] R. L. E. Schwarzenberger, Vector bundles on algebraic surfaces,Proc. Lond. Math. Soc. (3), vol. 11 (1961), 601–622. · Zbl 0212.26003 · doi:10.1112/plms/s3-11.1.601
[7] EGA,A. Grothendieck,Éléments de géométrie algébrique (rédigés avec la collaboration deJ. Dieudonné), Publications Mathématiques, Institut des Hautes Études Scientifiques (1960 ff).
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