Varchenko, A. N. The complex exponent of a singularity does not change along strata mu=const. (English. Russian original) Zbl 0498.32010 Funct. Anal. Appl. 16, 1-9 (1982); translation from Funkts. Anal. Prilozh. 16, No. 1, 1-12 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 84 Documents MSC: 32S30 Deformations of complex singularities; vanishing cycles 32C30 Integration on analytic sets and spaces, currents 32S05 Local complex singularities 32Sxx Complex singularities Keywords:rigidity of complex exponent of singularity; holomorphic differential n- form; Milnor number; deformations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. I. Arnol’d, ”Remarks on the method of stationary phase and the Coxeter numbers,” Usp. Mat. Nauk,28, No. 5, 17-44 (1973). [2] V. I. Arnol’d, ”Index of a singular point of a vector field, the Petrovskii?Oleinik inequalities and mixed Hodge structures,” Funkts. Anal.,12, No. 1, 1-14 (1978). [3] E. Brieskorn, ”Monodromy of isolated singularities of hypersurfaces,” Matematika,15, No. 4, 130-160 (1971). [4] A. N. Varchenko, ”Newton polyhedra and estimates of oscillating integrals,” Funkts. Anal.,10, No. 3, 13-38 (1976). [5] A. N. Varchenko, ”Hodge property of the Gauss?Manin connection,” Funkts. Anal.,14, No. 1, 46-47 (1980). [6] A. N. Varchenko, ”Asymptotics of holomorphic forms define the mixed Hodge structure,” Dokl. Akad. Nauk SSSR,255, No. 5, 1035-1038 (1980). · Zbl 0516.14007 [7] J. Leray, Differential and Integral Calculus on a Complex Analytic Manifold [Russian translation], IL, Moscow (1961). · Zbl 0111.10601 [8] R. O. Wells, Jr., Differential Analysis on Complex Manifolds, Prentice-Hall (1973). · Zbl 0262.32005 [9] C. H. Clemens, ”Degeneration of K?hler manifolds,” Duke Math. J.,44, No. 2, 215-290 (1977). · Zbl 0353.14005 · doi:10.1215/S0012-7094-77-04410-6 [10] P. Deligne, ”Theorie de Hodge. I,” in: Proc. Int. Congress Math. (Nice, 1970), Vol. 1, pp. 425-430; II, Publ. Math. IHES,40, 5-58 (1971); III, Publ. Math. IHES,44, 5-77 (1972). [11] P. A. Griffiths, ”Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems,” Bull. Am. Math. Soc.,76, 228-296 (1970). · Zbl 0214.19802 · doi:10.1090/S0002-9904-1970-12444-2 [12] P. A. Griffiths and W. Schmid, ”Recent development in Hodge theory, a discussion of techniques and results,” in: Proc. Int. Colloq. on Discrete Subgroups of Lie Groups, Bombay (1973), pp. 31-127. [13] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York (1970). [14] B. Malgrange, ”Integrales asymptotiques et monodromie,” Ann. Sci. Ecole Norm. Super.,7, 405-430 (1974). · Zbl 0305.32008 [15] W. Schmid, ”Variation of Hodge structures: the singularities of the period mappings,” Invent. Math.,22, 211-319 (1973). · Zbl 0278.14003 · doi:10.1007/BF01389674 [16] J. H. M. Steenbrink, ”Intersection form for quasihomogeneous singularities,” Compositio Math.,34, 211-223 (1977). · Zbl 0347.14001 [17] J. H. M. Steenbrink, ”Mixed Hodge structure on vanishing cohomology,” in: Nordic Summer School, Symposium in Math., Oslo, Aug. 5-25, 1976, pp. 525-563. [18] J. Scherk, ”On the monodromy theorem for isolated hypersurface singularities,” Invent. Math.,58, No. 3, 289-301 (1980). · Zbl 0432.32010 · doi:10.1007/BF01390256 [19] A. N. Varchenko, ”The Gauss?Manin connection of isolated singular point and Bernstein polynomial,” Bull. Sci. Math., 2e sec.,104, 205-223 (1980). · Zbl 0434.32008 [20] Le Dung Trang and C. P. Ramanujam, ”The invariance of Milnor’s number implies the invariance of topological type,” Am. J. Math.,98, 67-78 (1976). · Zbl 0351.32009 · doi:10.2307/2373614 [21] A. N. Varchenko, ”Asymptotic Hodge structure and vanishing cohomology,” Izv. Akad. Nauk SSSR, Ser. Mat.,45, 540-591 (1981). · Zbl 0476.14002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.