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An obstruction for smoothing of Gorenstein surface singularities

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Commentarii Mathematici Helvetici

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References

  • [D]Durfee, A.,The signature of smoothings of complex surface singularities, Math. Ann.232 (1978), 85–98.

    Article  MathSciNet  MATH  Google Scholar 

  • [FK]Freedman, M. andKirby, R.,A geometric proof of Rohlin's theorem. Proc. Symp. in Pure Math., Vol. XXXII part II, pp. 85–98.

  • [Ha]Hartshorne, R.,Topological conditions for smoothing algebraic singularities, Topology13 (1974), 241–253.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi]Hirzebruch, F.,Topological methods in algebraic geometry. Grundlehren131, Springer 1966.

  • [HNK]Hirzebruch, F., Neumann, W. andKoh, S. Differential manifolds and quadratic forms. Marcel Dekker, New York 1971.

    MATH  Google Scholar 

  • [L]Libgober, A.,Theta characteristics on singular curves spin structures and Rohlin Thoerem. Ann. Scient. Éc. Norm. Sup., 4e s'erie, t. 21, (1988).

  • [La1]Laufer H.,Taut two dimensional singularities, Math. Ann.205 (1973), 131–164.

    Article  MathSciNet  MATH  Google Scholar 

  • [La2]Laufer, H.,On rational singularities. Amer. J. Math., Vol. XCIV, No. 2, 597–608 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  • [La3]Laufer, H.,On u for surface singualrities. Symp. in Pure Math.30 (1977), 45–49.

    Article  MathSciNet  Google Scholar 

  • [Lo]Looijenga, E.,Riemann-Roch and smoothing of singularities. Topology25 (1986), 293–302.

    Article  MathSciNet  MATH  Google Scholar 

  • [LW]Looijenga, E. andWahl, J.,Quadratic functions and smoothing of singularities. Topology25 (1986), 261–291.

    Article  MathSciNet  MATH  Google Scholar 

  • [Mi]Milnor, J.,Spin structures on manifolds. L'Enseignment Math.9 (1963), 198–203.

    MathSciNet  MATH  Google Scholar 

  • [Mu]Mumford, D.,The topology of normal surface singularities of an algebraic surface and a criterion for simplicity. Publ. Math. IHES9 (1961), 5–22.

    Article  MathSciNet  MATH  Google Scholar 

  • [N]Neumann, W.,An invariant of plumbed homology spheres. Lecture Notes in Math., Vol. 788, pp. 125–144, Springer 1984.

  • [NR]Neumann, W. andRaymond, F.,Seifert manifolds plumbing, μ-invariant and orientation reversing maps. Algebraic and Geometric Topology. Proc. Santa Barbara 1977, Springer Lecture Notes664 (1978), 163–196.

  • [RT]Rees, E. andThomas, E.,Smoothings of isolated singularities. Proc. Symp. Pure Math.32 (1978), 111–117.

    Article  MathSciNet  MATH  Google Scholar 

  • [R]Guillou, L. andMarin, A., (eds)A la Recherche de la Topologie Perdue, I Du câté de chez Rohlin, II Le côté de Casson. Birkhäuser, 1986.

  • [S1]Seade, J.,A cobordism invariant for surface singularities. Proc. Symp. in Pure Math.40 part 2, (1983), 479–484.

    Article  MathSciNet  MATH  Google Scholar 

  • [S2]Seade, J.,Singular points of complex surfaces and homotopy. Topology21 (1982), 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  • [S]Schaps, M.,Deformations of Cohen Macauley schemes of codimension 2 and nonsingular deformations of space curves. Amer. J. Math.99 (1977), 669–685.

    Article  MathSciNet  MATH  Google Scholar 

  • [W]Wahl, J.,Smoothings of normal surface singularities. Topology20 (1981), 219–246.

    Article  MathSciNet  MATH  Google Scholar 

  • [Y1]Yau, S. S.-T.,The signature of Milnor fibres and duality theorem for strongly pseudoconvex manifolds. Invent. Math.46 (1978), 81–97.

    Article  MathSciNet  MATH  Google Scholar 

  • [Y2]Yau, S. S.-T.,Deformations and equitopological deformations of strongly pseudoconvex manifolds. Nagoya Math. J.82 (1981), 113–129.

    Article  MathSciNet  MATH  Google Scholar 

  • [Y3]Yau, S. S.-T.,Various numerical invariants for isolated singularities. Amer. J. Math.104 (1982), 1063–1110.

    Article  MathSciNet  MATH  Google Scholar 

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Libgober, A., Yau, S.S.T. An obstruction for smoothing of Gorenstein surface singularities. Commentarii Mathematici Helvetici 65, 413–433 (1990). https://doi.org/10.1007/BF02566616

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