Acta Mathematica

, Volume 135, Issue 1, pp 155–185 | Cite as

Embedding-obstruction for singular algebraic varieties inP N

  • Audun Holme
Article

Keywords

Algebraic Variety Singular Algebraic Variety 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1].
    Altman, A. B. & Kleiman, S. L., Joins of schemes. To appear.Google Scholar
  2. [2].
    Baum, P., Fulton, W. & MacPherson, R., Riemann-Roch for singular varieties. To appear.Google Scholar
  3. [3].
    Grothendieck, A. (with the colloboration of Dieudonné, J.),Éléments de géométrie algébrique. Chapter I–IV. Publications Mathématiques, Institut des Hautes Études Scientifiques, 4, 8, 11, 17, 20, 24, 28, 32. Paris 1960–1967. (Referred to as EGA.)Google Scholar
  4. [4].
    Hartshorne, R., Varieties of small codimension in projective space. (An expanded version of talk presented to the summer meeting of the A.M.S. Missoula, August 1973.)Bull. Amer. Math. Soc., 80 (1974), 1017–1032.MATHMathSciNetCrossRefGoogle Scholar
  5. [5].
    —, Equivalence relations on algebraic cycles and subvarieties of small codimension.Algebraic geometry. (Prod. sympos. pure math. Vol 29, Humboult State Univ., Arcata. California 1974) 129–164. AMS Providence 1975.Google Scholar
  6. [6].
    Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero.Ann. of Math., 79 (1964), 109–326.CrossRefMATHMathSciNetGoogle Scholar
  7. [7].
    —, Certain numerical characters of singularities.J. Math. Kyoto Univ. 10 (1970), 151–187.MATHMathSciNetGoogle Scholar
  8. [8].
    Holme, A., Projection of non-singular projective varieties.J. Math. Kyoto Univ. 13 (1973), 301–322.MATHMathSciNetGoogle Scholar
  9. [9].
    —, An embedding-obstruction for algebraic varieties (research announcement).Bull. Amer. Math. Soc., 80 (1974), 932–934.MATHMathSciNetGoogle Scholar
  10. [10].
    Holme, A., Embedding-obstruction for smooth, projective varieties. To appear inAdvances in Math. Google Scholar
  11. [11].
    Ilori, S. A., Ingleton, A. W. &Lascu, A. T., On a formula of D. B. Scott.J. London Math. Soc., (2), 8 (1974), 539–544.MathSciNetMATHGoogle Scholar
  12. [12].
    Kleiman, S. L. &Landolfi, J., Geometry and deformation of special Schubert varieties.Algebraic geometry, Oslo 1970 (Oort, F., editor.) Wolters-Noordhoff Publishing, Groningen, 1972.Google Scholar
  13. [13].
    Lluis, E., Sur l'immersion des variétés algébriques.Ann. of Math., 62 (1955), 120–127.CrossRefMATHMathSciNetGoogle Scholar
  14. [14].
    —, De las singularidades que aparecen al proyectar variedades algebraicas.Bol. Soc. Mat. Mexicana, 1 (1956), 1–9.MATHMathSciNetGoogle Scholar
  15. [15].
    MacPherson, R. D., Chern classes for singular algebraic varieties.Ann. of Math., 100 (1974), 423–432.CrossRefMATHMathSciNetGoogle Scholar
  16. [16].
    Peters, C. A. M. & Simons, J., A secant formula. To appear.Google Scholar
  17. [17].
    Roberts, J., Generic projections of algebraic varieties.Amer. J. Math., 93 (1971), 119–215.Google Scholar
  18. [18].
    —, The variation of critical cycles in algebraic families.Trans. Amer. Math. Soc., 168 (1972), 153–164.CrossRefMATHMathSciNetGoogle Scholar
  19. [19].
    Schwarzenberger, R. L. E., The secant bundle of a projective variety.Proc. London Math. Soc., (3) 14 (1964), 369–384.MATHMathSciNetGoogle Scholar
  20. [20].
    Swan, R. G., A cancellation theorem for projective modules in the metastable range.Invent. Math., 27, (1974), 23–43.CrossRefMATHMathSciNetGoogle Scholar
  21. [21].
    Swinnerton-Dyer, H. P. F., An enumeration of all varieties of degree 4.Amer. J. Math., 95 (1973), 403–418.MATHMathSciNetGoogle Scholar
  22. [22].
    Szpiro, L.:Cohomologie des ouverts de l'espace projectif sur un corps de caracteristique zéro [d'après A. Ogus], Sém. Bourbaki, exposé 458, novembre 1974.Google Scholar
  23. [23].
    X. X. X. Correspondence,Amer. J. Math., 79 (1957), 951–952.Google Scholar

Copyright information

© Almqvist & Wiksell 1975

Authors and Affiliations

  • Audun Holme
    • 1
  1. 1.University of BergenNorway

Personalised recommendations