Acta Mathematica

Multiple-point formulas I: Iteration

Steven L. Kleiman

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J. S. Guggenheim Fellow. This work was supported in part by NSF MCS-7906895.

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Acta Math. Volume 147 (1981), 13-49.

Received: 15 July 1980
First available in Project Euclid: 31 January 2017

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1981 © Almqvist & Wiksell


Kleiman, Steven L. Multiple-point formulas I: Iteration. Acta Math. 147 (1981), 13--49. doi:10.1007/BF02392866.

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  • Altman, A. & Kleiman, S., Compactifying the Picard scheme. Advances in Math., 35: 1 (1980), 50–112.
  • Artin, M. & Nagata, M., Residual intersections in Cohen-Macauley rings. J. Math. Kyoto Univ., 12 (1972), 307–323.
  • EGA II, IV1, IV2, IV4, Eléments de géométrie algébrique. A. Grothendieck and J. Dieudonné. Inst. Hautes Etudes Sci. Publ. Math., Nos. 8 (1961), 20 (1964), 24 (1965), 32 (1967).
  • Fultön, W., A note on residual intersections and the double point formula. Acta math., 140 (1978), 93–101.
  • Fulton, W. & Laksov, D., Residual intersections and the double point formula. Real and complex singularities, Oslo 1976. P. Holm, ed., pp. 171–177. Sijthoff & Noordhooff (1977).
  • Fulton, W. & MacPherson, Bivariant theories. Preprint, Brown Univ., Providence (1980).
  • Herbert, R., Multiple points of immersed manifolds. Thesis, Univ. of Minnesota (1975).
  • Huneke, C., On the symmetric and Rees algebra of an ideal generated by a d-sequence. To appear in a volume of the J. Alg. dedicated to N. Jacobson.
  • Johnson, K., Immersion and embedding of projective varieties. Acta math., 140 (1978), 49–74.
  • Kleiman, S., The enumerative theory of singularities. Real and complex singularities, Oslo 1976. P. Holm ed., pp. 297–396. Sijthoff & Noordhoof (1977).
  • Kleiman, S. Multiple-point formulas for maps. To appear.
  • Kleiman, S., Multiple-point formulas II: The Hilbert scheme. In preparation.
  • Laksov, D., Residual intersections and Todd's formula for the double locus of a morphism. Acta math., 140 (1978), 75–92.
  • —, Secant bundles and Todd's formula for the double points of maps into Pn. Proc. Lond. Math. Soc., 37 (1978), 120–142.
  • Lichtenbaum, S. & Schlessinger, M., The cotangent complex of a morphism. Trans. Amer. Math. Soc., 128: 1 (1967), 41–70.
  • Micali, A., Algebra symétrique d'un idéal. C. R. Acad. Sci. Paris, 251 (1960), 1954–1956.
  • Piene, R. & Ronga, F., A geometric approach to the arithmetic genus of a projective manifold of dimension three. Preprint, July (1979).
  • Roberts, J., Some properties of double point schemes. Preprint May (1979). To appear in Compositio math.
  • Ronga, F., Le calcul des classes duales aux points doubles d'une application, Compositio math., 27: 2 (1973), 223–232.
  • Ronga, F., On multiple points of smooth immersions. Preprint March (1980).
  • SGA6, Théorie des Intersections et Théorème de Riemann-Roch. P. Berthelot et al. Lecture Notes in Math. No. 225, Springer (1971).