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Semicontinuity of the singularity spectrum

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References

  • [A] Arnol'd, V.I.: On some problems in singularity theory. Geometry and Analysis, Papers dedicated to the memory of V.K. Patodi, Bombay 1981, pp. 1–10

  • [B] du Bois, Ph.: Structure de Hodge mixte sur la cohomologie évanescente. Ann. Inst. Fourier (to appear)

  • [D] Deligne, P.: Théorie de Hodge. II. Publ. Math. IHES40, 5–58 (1971); III Publ. Math. IHES44, 5–75 (1975)

    Google Scholar 

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

    Google Scholar 

  • [E] Elkik, R.: Singularités rationelles et déformations. Invent. Math.47, 139–147 (1978)

    Google Scholar 

  • [EZ] El Zein, F.: Dégénérescence diagonale. I. C.R. Acad. Sc. Paris276, 51–54 (1983); II. C.R. Acad. Sc. Paris276, 199–202 (1983)

    Google Scholar 

  • [G] Greuel, G.-M.: Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten. Math. Ann.214, 235–266 (1975)

    Google Scholar 

  • [GNP] Guillén, F., Navarro Aznar, V., Puerta, F.: Théorie de Hodge via schémas cubiques. Mimeographed notes, Barcelona 1982

  • [GS] Greuel, G.-M., Steenbrink, J.H.M.: On the topology of smoothable singularities. Proc. Symp. Pure Math.40, Part I, 535–545 (1983)

    Google Scholar 

  • [M] Milnor, J.: Singular points of complex hypersurfaces. Annals of Math. Studies vol. 61, Princeton 1968

  • [Ma] Malgrange, B.: Intégrales asymptotiques et monodromie. Ann. Sc. Éc. Norm. Sup. 4e série,7, 405–430 (1974)

    Google Scholar 

  • [Sc] Schmid, W.: Variation of Hodge structure: the singularities of the period mapping. Invent. Math.22, 211–320 (1973)

    Google Scholar 

  • [S1] Steenbrink, J.H.M.: Mixed Hodge structure on the vanishing cohomology. Real and complex singularities, Oslo 1976. Sijthoff-Noordhoff 1977, pp. 525–563

  • [S2] Steenbrink, J.H.M.: Mixed Hodge structures associated with isolated singularities. Proc. Symp. Pure Math.40, Part II, 513–536 (1983)

    Google Scholar 

  • [SZ] Steenbrink, J.H.M., Zucker, S.: Variation of mixed Hodge structure I. Univ. of Leiden, Report 2, Jan. 1984

  • [V1] Varchenko, A.N.: The complex exponent of a singularity does not change along strata μ =const. Funct. An. Appl.16, 1–10 (1982)

    Google Scholar 

  • [V2] Varchenko, A.N.: On semicontinuity of the spectrum and an upper bound for the number of singular points of projective hypersurfaces. Dokladyi Ak. Nauk.270 (6) 1294–1297 (1983)

    Google Scholar 

  • [V3] Varchenko, A.N.: Asymptotics of integrals and Hodge structures. In: Modern Problems of Mathematics, vol.22, pp. 130–166 (1983) (in Russian)

  • [V4] Varchenko, A.N.: On change of discrete invariants of critical points of functions under deformation. Uspehi Mat. Nauk.5, 126–127 (1983)

    Google Scholar 

  • [V5] Varchenko, A.N.: On semicontinuity of the complex singularity index. Funct. An. Appl.17, 77–78 (1983)

    Google Scholar 

  • [V6] Varchenko, A.N.: Asymptotic Hodge structure in the vanishing cohomology. Math. USSR Izvestija18, 469–512 (1982)

    Google Scholar 

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Steenbrink, J.H.M. Semicontinuity of the singularity spectrum. Invent Math 79, 557–565 (1985). https://doi.org/10.1007/BF01388523

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