×

zbMATH — the first resource for mathematics

Lifting cycles to deformations of two-dimensional pseudoconvex manifolds. (English) Zbl 0512.32017

MSC:
32G10 Deformations of submanifolds and subspaces
14C99 Cycles and subschemes
32T99 Pseudoconvex domains
14D20 Algebraic moduli problems, moduli of vector bundles
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. Artin, Algebraic construction of Brieskorn’s resolutions, J. Algebra 29 (1974), 330 – 348. · Zbl 0292.14013 · doi:10.1016/0021-8693(74)90102-1 · doi.org
[2] M. Artin and M. Schlessinger, Algebraic construction of Brieskorn’s resolutions, preprint. · Zbl 0292.14013
[3] A. Douady, Le problème des modules locaux pour les espaces \?-analytiques compacts, Ann. Sci. École Norm. Sup. (4) 7 (1974), 569 – 602 (1975) (French). · Zbl 0313.32036
[4] Renée Elkik, Algébrisation du module formel d’une singularité isolée, Quelques problèmes de modules (Sém. Géom. Anal., École Norm. Sup., Paris, 1971-1972) Soc. Math. France, Paris, 1974, pp. 133 – 144. Astérisque, No. 16 (French). · Zbl 0294.14008
[5] Wolfgang Fischer and Hans Grauert, Lokal-triviale Familien kompakter komplexer Mannigfaltigkeiten, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1965 (1965), 89 – 94 (German). · Zbl 0135.12601
[6] Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331 – 368 (German). · Zbl 0173.33004 · doi:10.1007/BF01441136 · doi.org
[7] Hans Grauert, Über die Deformation isolierter Singularitäten analytischer Mengen, Invent. Math. 15 (1972), 171 – 198 (German). · Zbl 0237.32011 · doi:10.1007/BF01404124 · doi.org
[8] Hans Grauert, Der Satz von Kuranishi für kompakte komplexe Räume, Invent. Math. 25 (1974), 107 – 142 (German). · Zbl 0286.32015 · doi:10.1007/BF01390171 · doi.org
[9] R. C. Gunning and Raghavan Narasimhan, Immersion of open Riemann surfaces, Math. Ann. 174 (1967), 103 – 108. · Zbl 0179.11402 · doi:10.1007/BF01360812 · doi.org
[10] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. · Zbl 0141.08601
[11] Arnold Kas and Michael Schlessinger, On the versal deformation of a complex space with an isolated singularity, Math. Ann. 196 (1972), 23 – 29. · Zbl 0242.32014 · doi:10.1007/BF01419428 · doi.org
[12] K. Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math. (2) 75 (1962), 146 – 162. · Zbl 0112.38404 · doi:10.2307/1970424 · doi.org
[13] K. Kodaira and D. C. Spencer, A theorem of completeness of characteristic systems of complete continuous systems, Amer. J. Math. 81 (1959), 477 – 500. · Zbl 0097.36501 · doi:10.2307/2372752 · doi.org
[14] Henry B. Laufer, On rational singularities, Amer. J. Math. 94 (1972), 597 – 608. · Zbl 0251.32002 · doi:10.2307/2374639 · doi.org
[15] Henry B. Laufer, Deformations of resolutions of two-dimensional singularities, Rice Univ. Studies 59 (1973), no. 1, 53 – 96. Complex analysis, 1972, Vol. I: Geometry of singularities (Proc. Conf., Rice Univ., Houston, Tex., 1972).
[16] Henry B. Laufer, Taut two-dimensional singularities, Math. Ann. 205 (1973), 131 – 164. · Zbl 0281.32010 · doi:10.1007/BF01350842 · doi.org
[17] -, Ambient deformations for one-dimensional exceptional sets, 1978, preprint.
[18] Henry B. Laufer, Ambient deformations for exceptional sets in two-manifolds, Invent. Math. 55 (1979), no. 1, 1 – 36. · Zbl 0509.32010 · doi:10.1007/BF02139700 · doi.org
[19] Henry B. Laufer, Versal deformations for two-dimensional pseudoconvex manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 3, 511 – 521. · Zbl 0512.32016
[20] Henry B. Laufer, On \?\?\textonesuperior as an exceptional set, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 261 – 275.
[21] Lê Dũng Tráng and C. P. Ramanujam, The invariance of Milnor’s number implies the invariance of the topological type, Amer. J. Math. 98 (1976), no. 1, 67 – 78. · Zbl 0351.32009 · doi:10.2307/2373614 · doi.org
[22] Geneviève Pourcin, Déformation de singularités isolées, Quelques problèmes de modules (Sém. Géom. Anal., École Norm. Sup., Paris, 1971 – 1972) Soc. Math. France, Paris, 1974, pp. 161 – 173. Astérisque, No. 16 (French). · Zbl 0292.32014
[23] Oswald Riemenschneider, Familien komplexer Räume mit streng pseudokonvexer spezieller Faser, Comment. Math. Helv. 51 (1976), no. 4, 547 – 565. · Zbl 0338.32013 · doi:10.1007/BF02568173 · doi.org
[25] Bernard Teissier, Déformations à type topologique constant, Quelques problèmes de modules (Sém. de Géométrie Analytique, École Norm. Sup., Paris, 1971 – 1972) Soc. Math. France, Paris, 1974, pp. 215 – 249. Astérisque, No. 16 (French). · Zbl 0301.32013
[26] Jonathan M. Wahl, Equisingular deformations of normal surface singularities. I, Ann. of Math. (2) 104 (1976), no. 2, 325 – 356. · Zbl 0358.14007 · doi:10.2307/1971049 · doi.org
[27] -, The discriminant locus of a rational singularity, informal research announcement, 1976.
[28] Jonathan M. Wahl, Simultaneous resolution and discriminantal loci, Duke Math. J. 46 (1979), no. 2, 341 – 375. · Zbl 0472.14002
[29] Hassler Whitney, Tangents to an analytic variety, Ann. of Math. (2) 81 (1965), 496 – 549. · Zbl 0152.27701 · doi:10.2307/1970400 · doi.org
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.