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Two theorems on higher dimensional singularities. (English) Zbl 0343.32010

32Sxx Complex singularities
32S45 Modifications; resolution of singularities (complex-analytic aspects)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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[1] Arnold, V.: Normal forms for functions near degenerate critical points, the Weyl groups ofA k,D k,E k, and Lagrangian singularities. Func. Anal. App.6 (1972)
[2] Artin, M.: On isolated rational singularities of surfaces. Amer. J. Math.88, 129-136 (1964) · Zbl 0142.18602
[3] Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math. I.H.E.S.36 (1969) · Zbl 0181.48802
[4] Brieskorn, E.: Rationale Singularitäten Komplexer Flächen. Inv. Math.4, 336-358 (1967/68) · Zbl 0219.14003
[5] Burns, D.: On Rational Singularities in Dimensions >2. Math. Ann.211, 237-244 (1974) · Zbl 0287.32010
[6] DuVal, P.: On isolated singularities of surfaces which do not affect the conditions of adjunction. I. Proc. Cambridge Philos. Soc.30, 453-459 (1934) · JFM 60.0599.01
[7] Grauert, H., Riemenschneider, O.: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen. Invent. Math.11, 263-292 (1970) · Zbl 0202.07602
[8] Gunning, R., Rossi, H.: Analytic functions of several variables. Englewood Cliffs, N.J.: Prentice-Hall 1965 · Zbl 0141.08601
[9] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic 0. I?II. Ann. Math.79 (1964) · Zbl 0122.38603
[10] Laufer, H.: On minimally elliptic singularities. Amer. J. Math. (to appear) · Zbl 0384.32003
[11] Laufer, H.: On rational singularities. Amer. J. Math.94, 597-608 (1972) · Zbl 0251.32002
[12] Lipman, J.: Rational singularities with applications to algebraic surfaces and unique factorizations. Publ. Math. I.H.E.S.36, 195-279 (1969) · Zbl 0181.48903
[13] Siu, Y.-T.: Absolute gap Sheaves and extension of coherent analytic sheaves. Trans. AMS141, 361-376 (1969) · Zbl 0184.11001
[14] Tyurina, G.N.: Absolute isolatedness of rational singularities and triple rational points. Func. Anal. App.2, 324-332 (1968) · Zbl 0176.50804
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