Bulletin of the American Mathematical Society

Nonsmoothing of algebraic cycles on Grassmann varieties

Robin Hartshorne, Elmer Rees, and Emery Thomas

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 80, Number 5 (1974), 847-851.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183535816

Mathematical Reviews number (MathSciNet)
MR0357402

Zentralblatt MATH identifier
0289.14011

Subjects
Primary: 14C10 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture 55G10
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 55F40

Citation

Hartshorne, Robin; Rees, Elmer; Thomas, Emery. Nonsmoothing of algebraic cycles on Grassmann varieties. Bull. Amer. Math. Soc. 80 (1974), no. 5, 847--851. https://projecteuclid.org/euclid.bams/1183535816


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References

  • 1. A. 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. MR 14, 490.
  • 2. A. Borel and A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France 89 (1961), 461-513. MR 26 #6990.
  • 3. A. Borel and J.-P. Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953), 409-448. MR 15, 338.
  • 4. C. Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. 35 (1934), 396-443.
  • 5. D. B. A. Epstein, Steenrod operations in homological algebra, Invent. Math. 1 (1966), 152-208. MR 33 #7389.
  • 6. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-326. MR 33 #7333.
  • 7. H. Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math. 90 (1968), 1-54. MR 37 #210.
  • 8. S. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes Études Sci. Publ. Math. No. 36 (1969), 281-297. MR 42 #281.
  • 9. S. Kleiman and J. Landolfi, Geometry and deformation of special Schubert varieties, Compositio Math. 23 (1971), 407-434.
  • 10. M. Raynaud, Modules projectifs universels, Invent. Math. 6 (1968), 1-26.
  • 11. R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 15, 890.