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Nonsmoothing of algebraic cycles on Grassmann varieties. (English) Zbl 0289.14011


MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14C15 (Equivariant) Chow groups and rings; motives
57R10 Smoothing in differential topology
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References:

[1] Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115 – 207 (French). · Zbl 0052.40001
[2] Armand Borel and André Haefliger, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France 89 (1961), 461 – 513 (French). · Zbl 0102.38502
[3] A. Borel and J.-P. Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953), 409 – 448 (French). · Zbl 0050.39603
[4] Charles Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. (2) 35 (1934), no. 2, 396 – 443 (French). · JFM 60.1223.05
[5] D. B. A. Epstein, Steenrod operations in homological algebra, Invent. Math. 1 (1966), 152 – 208. · Zbl 0139.01502
[6] Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109 – 203; ibid. (2) 79 (1964), 205 – 326. · Zbl 0122.38603
[7] Heisuke Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math. 90 (1968), 1 – 54. · Zbl 0173.22801
[8] Steven L. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 281 – 297. · Zbl 0208.48501
[9] Steven L. Kleiman and John Landolfi, Geometry and deformation of special Schubert varieties, Compositio Math. 23 (1971), 407 – 434. · Zbl 0238.14006
[10] Michèle Raynaud, Modules projectifs universels, Invent. Math. 6 (1968), 1 – 26 (French). · Zbl 0216.32601
[11] René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17 – 86 (French). · Zbl 0057.15502
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