×

On pencils of curves and deformations of minimally elliptic singularities. (English) Zbl 0407.14014


MSC:

14J17 Singularities of surfaces or higher-dimensional varieties
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14H10 Families, moduli of curves (algebraic)
14D15 Formal methods and deformations in algebraic geometry

Citations:

Zbl 0314.17013
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Andreotti, A., Vesentini, E.: On the pseudo-rigidity of Stein manifolds. Ann. Sculo Norm. sup. Pisa16, 213-233 (1962) · Zbl 0107.28602
[2] Arnold, V.I.: Normal forms of functions. Invent. math.35, 87-109 (1976) · Zbl 0336.57022
[3] Artin, M.: On isolated rational singularities of surfaces. Amer. J. Math.88, 129-136 (1966) · Zbl 0142.18602
[4] Artin, M.: Algebraic construction of Brieskorn’s resolutions. J. Algebra29, 330-348 (1974) · Zbl 0292.14013
[5] Brieskorn, E.: Rationale Singularitäten komplexer Flächen. Invent. math.6, 336-358 (1967/68)
[6] Brieskorn, E.: Die Hierarchie der 1-Modularen Singularitäten. Preprint Bonn, 1978 · Zbl 0406.58009
[7] Forster, O., Knorr, K.: Ein neuer Beweis des Satzes von Kodaira-Nierenberg-Spencer. Math. Z.139, 257-291 (1974) · Zbl 0287.32014
[8] Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331-368 (1962) · Zbl 0173.33004
[9] Grauert, H.: Der Satz von Kuranishi für kompakte komplexe Räume. Invent. math.15, 107-142 (1974) · Zbl 0286.32015
[10] Karras, U.: Klassifikation 2-dimensionaler Singularitäten mit auflösbaren lokalen Fundamentalgruppen. Math. Ann.213, 231-255 (1975) · Zbl 0285.57019
[11] Karras, U.: Deformations of cusp singularities. Proceedings of Symposia in Pure Mathematics30, 37-44 (1977) · Zbl 0352.14007
[12] Karras, U.: On pencils of curves and surface singularities. Preprint, Purdue University, West-Lafayette 1977 · Zbl 0352.14007
[13] Karras, U.: Über Familien komplexer Kurven und Deformationen zwei-dimensionaler Singularitäten (in Vorbereitung)
[14] Kreyszig, E.: Stetige Modifikationen komplexer Mannigfaltigkeiten. Math. Ann.128, 479-492 (1955) · Zbl 0064.08002
[15] Kulikov, V.: Degenerate elliptic curves and resolution of uni- and bimodal singularities. Functional Anal. Appl.9, 69-70 (1975) · Zbl 0317.14013
[16] Kodaira, K.: On compact analytic surfaces. II. Ann. of Math.77, 563-626 (1963) · Zbl 0118.15802
[17] Kodaira, K.: On stability of compact submanifolds of complex manifolds. Amer. J. Math.85, 79-94 (1963) · Zbl 0173.33101
[18] Laufer, H.: Deformations of resolutions of two-dimensional singularities. Rice Univ. Studies59, 53-96 (1973) · Zbl 0281.32009
[19] Laufer, H.: Taut two-dimensional singularities. Math. Ann.205, 131-164 (1973) · Zbl 0281.32010
[20] Laufer, H.: On ? for surface singularities. Proc. Symposia Pure Math.30, 45-49 (1977) · Zbl 0363.32009
[21] Laufer, H.: Minimally elliptic singularities. Amer. J. Math.99, 1257-1295 (1978) · Zbl 0384.32003
[22] Laufer, H.: Ambient deformations for one-dimensional exceptional sets. Preprint 1978
[23] Leistner, D.: Vollständigkeitssatz für Deformationen von streng pseudokonvexen Mannigfaltigkeiten. Preprint 1976
[24] Lejeune, M., Teissier, B.: Normal cones and sheaves of relative jets. Compositio Math.28, 305-331 (1974) · Zbl 0337.14013
[25] Pinkham, H.: Deformations of algebraic varieties withG m action. Astérisque20, 1-131 (1974) · Zbl 0304.14006
[26] Pinkham, H.: Deformations of normal surface singularities with ?* action. Math. Ann.232, 65-84 (1978) · Zbl 0358.14005
[27] Riemenschneider, O.: Familien komplexer Räume mit streng pseudokonvexer spezieller Faser. Comment. Math. Helv.39, 547-565 (1977) · Zbl 0338.32013
[28] Riemenschneider, O.: Halbstetigkeitssätze für 1-konvexe holomorphe Abbildungen. Math. Ann.192, 216-226 (1971) · Zbl 0209.38802
[29] Teissier, B.: Deformations à type topologique constant. I. Astérisque16, 215-227 (1974) · Zbl 0301.32013
[30] Wagreich, P.: Elliptic singularities of surfaces. Amer. J. Math.92, 419-454 (1970) · Zbl 0204.54501
[31] Wahl, J.: Equisingular deformations of normal surface singularities. I. Ann. of Math.104, 325-356 (1976) · Zbl 0358.14007
[32] Wahl, J.: Equations defining rational singularities. Ann. scient. Éc. Norm. Sup.10, 231-264 (1977) · Zbl 0367.14004
[33] Wahl, J.: Simultaneous resolution and discriminantal loci. Preprint 1978 · Zbl 0472.14002
[34] Winters, G.: On the existence of certain families of curves. Amer. J. Math.96, 215-228 (1974) · Zbl 0334.14004
[35] Yau, S.T.: On maximally elliptic singularities. Preprint 1977 · Zbl 0365.32006
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.