Some formulas for a surface in ℙ3

  • Ragni Piene
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 687)


Triple Point Double Point Generic Projection Singular Locus Smooth Point 
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  1. [A]
    M. Artin, On Enriques Surfaces, Doctoral thesis, Harvard University, 1960.Google Scholar
  2. [B]
    H.F. Baker, Principles of geometry. Vol.VI. Introduction to the theory of algebraic surfaces and higher loci. Cambridge Univ.Press, 1933.Google Scholar
  3. [F]
    W. Fulton, "Rational equivalence on singular varieties". Publ.Math.IHES, 45 (1976), Paris.Google Scholar
  4. [K-L]
    G. Kempf, D. Laksov, "The determinantal formula of Schubert calculus". Acta Math., 132 (1974), 153–162.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [K]
    S. Kleiman, "The enumerative theory of singularities". Proceedings of the Nordic Summer School, Oslo 1976(Noordhoff).Google Scholar
  6. [La]
    D. Laksov, "Secant bundles and Todd's formula for the double points of maps into ℙn". Preprint, M.I.T., 1976.Google Scholar
  7. [L1]
    E. Lluis, "De las singularidades que aparacen al proyectar variedades algebraicas". Bol.Soc.Mat. Mexicana, Ser. 2, 1 (1956), 1–9.MathSciNetGoogle Scholar
  8. [N]
    M. Noether, "Sulle curve multiple di superficie algebriche". Ann.d.Mat., 5 (1871–3), 163–177.CrossRefzbMATHGoogle Scholar
  9. [P1]
    R. Piene, "Polar classes of singular varieties". Ann, scient. Éc. Norm. Sup. t. 11, 1978, fasc. 2.Google Scholar
  10. [P2]
    R. Piene, "A proof of Noether's formula for the arithmetic genus of an algebraic surface". Preprint, M.I.T., 1977.Google Scholar
  11. [P3]
    R.Piene, "Numerical characters of a curve in projective n-space". Proceedings of the Nordic Summer School, Oslo 1976 (Noordhoff).Google Scholar
  12. [R1]
    J. Roberts, "Generic projections of algebraic varieties". Am.J.Math., 93 (1971), 191–215.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [R2]
    J. Roberts, "Singularity subschemes and generic projections". Trans.AMS, 212 (1975), 229–268.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [R3]
    J. Roberts, "Variations of singular cycles in an algebraic family of morphisms". Trans.AMS, 168 (1972), 153–164.CrossRefzbMATHGoogle Scholar
  15. [R]
    L. Roth, "Some formulae for primals in four dimensions". Proc. London Math.Soc., Ser. 2, 35 (1933), 540–550.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [S]
    G. Salmon, A treatise on the analytic geometry of three dimensions. Vol. II, 5th ed., Dublin 1915.Google Scholar
  17. [SAG 7]
    N. Katz, "Pinceaux de Lefschetz: théorème d'existence". Exp. XVII in SGA 7, II, Springer L.N.M., 340.Google Scholar
  18. [S-R]
    J.G. Semple, S. Roth, Introduction to algebraic geometry. Oxford 1949.Google Scholar
  19. [V]
    I. Vainsencher, On the formula of de Jonquières for multiple contacts. Doctoral thesis, M.I.T., 1976.Google Scholar
  20. [W]
    A. Wallace, "Tangency and duality over arbitrary fields". Proc. London Math.Soc., Ser. 3, 6 (1956), 321–342.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [Z]
    H.G. Zeuthen, "Révision et extension des formules numériques de la théorie des surfaces réciproques". Math.Ann., 10 (1876), 446–546.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Ragni Piene
    • 1
  1. 1.Institute of MathematicsUniversity of OsloOslo 3Norway

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