Duke Mathematical Journal

Modification de Nash et invariants numériques d’une surface normale

M. Vaquie

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Duke Math. J., Volume 57, Number 1 (1988), 69-84.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32B30
Secondary: 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45] 14J17: Singularities [See also 14B05, 14E15] 32C20: Normal analytic spaces


Vaquie, M. Modification de Nash et invariants numériques d’une surface normale. Duke Math. J. 57 (1988), no. 1, 69--84. doi:10.1215/S0012-7094-88-05703-1. https://projecteuclid.org/euclid.dmj/1077306849

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  • [B-F-MP] P. Baum, W. Fulton, and R. MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. (1975), no. 45, 101–145.
  • [B-G] R. O. Buchweitz and G. M. Greuel, The Milnor number and deformations of complex curve singularities, Invent. Math. 58 (1980), no. 3, 241–281.
  • [Du] A. Dubson, Classes caractéristiques des variétés singulières, C. R. Acad. Sci. Paris Sér. A-B 287 (1978), no. 4, A237–A240.
  • [G] G. Gonzalez-Sprinberg, Une formule pour les singularités isolées de surfaces, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 10, A475–A478.
  • [L] H. Laufer, On $\mu$ for surface singularities, Several Complex Variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975), vol. 30, Amer. Math. Soc., Providence, R. I., 1977, pp. 45–49.
  • [Lê-T] D. T. Lê and B. Teissier, Variétés polaires locales et classes de Chern des variétés singulières, Ann. of Math. (2) 114 (1981), no. 3, 457–491.
  • [MP] R. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432.
  • [Mi] J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., no. 61, Princeton University Press, Princeton, New Jersey, 1968.
  • [Mo] M. Morales, Calcul de quelques invariants des singularités de surface normale, Knots, braids and singularities (Plans-sur-Bex, 1982), Monogr. Enseign. Math., vol. 31, Enseignement Math., Geneva, 1983, pp. 191–203.
  • [N] A. Nobile, Some properties of the Nash blowing-up, Pacific J. Math. 60 (1975), no. 1, 297–305.
  • [P1] R. Piene, Cycles polaires et classes de Chern pour les variétés projectives singulières, prépubl., Centre de Math., École Polytechnique, 1978.
  • [P2] R. Piene, Ideals associated to a desingularization, Algebraic Geometry (Proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978), Lecture Notes in Math., vol. 732, Springer, Berlin, 1979, pp. 503–517.
  • [Ra] C. P. Ramanujam, On a geometric interpretation of multiplicity, Invent. Math. 22 (1973), 63–67.
  • [Re] M. Reid, Bogomolov's theorem $c_1^2\leq 4c_2$, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store, Tokyo, 1978, pp. 623–642.
  • [S1] J. Steenbrink, Limits of Hodge structures, Invent. Math. 31 (1976), no. 3, 229–257.
  • [S2] J. Steenbrink, Mixed Hodge structures associated with isolated singularities, Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 513–536.
  • [T] B. Teissier, Cycles évanescents, sections planes et conditions de Whitney, Singularités à Cargèse (Rencontre Singularités Géom. Anal., Inst. Études Sci., Cargèse, 1972), Astérisque, vol. 7-8, Soc. Math. France, Paris, 1973, pp. 285–362.
  • [W] J. Wahl, Smoothings of normal surface singularities, Topology 20 (1981), no. 3, 219–246.