On the invariance of -convexity and hyperconvexity under finite holomorphic surjections
Authors:
Nguyẽn Văn Khuê and Lê Văn Thành
Journal:
Trans. Amer. Math. Soc. 302 (1987), 47-54
MSC:
Primary 32F10; Secondary 32H35
DOI:
https://doi.org/10.1090/S0002-9947-1987-0887495-2
MathSciNet review:
887495
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Abstract: In this note we have proved that 0-convexity and hyperconvexity are invariant under finite holomorphic surjections. Invariance of cohomological -convexity for the case of finite dimension also has been established.
- [1] A. Andreotti and H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259. MR 0150342 (27:343)
- [2] H. Cartan, Quotients of complex spaces, Contributions to Function Theory, Tata Inst. of Fund. Res., Bombay, 1960, pp. 1-15. MR 0139769 (25:3199)
- [3] K. Diederich and J. E. Fornaess, Pseudoconvex domain: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. MR 0437806 (55:10728)
- [4] G. Fischer, Complex analytic geometry, Springer-Verlag, Berlin and New York, 1976. MR 0430286 (55:3291)
- [5] J. E. Fornaess and R. Narasimhan, The Levi problem on complex spaces with singularities, Math. Ann. 243 (1980), 47-72. MR 569410 (81f:32020)
- [6] B. Malgrange, Ideal of differentiable functions, Oxford Univ. Press, 1966. MR 0212575 (35:3446)
- [7] A. Markoe, Invariant of holomorphic convexity, Math. Ann. 217 (1975), 267-270. MR 0385169 (52:6034)
- [8] R. Narasimhan, A note on Stein spaces and their normalizations, Ann. Scuola Norm. Sup. Pisa 16 (1962), 327-333. MR 0153870 (27:3831)
- [9] -, The Levi problem for complex spaces. II, Math. Ann. 146 (1962), 195-216. MR 0182747 (32:229)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1987-0887495-2
Article copyright:
© Copyright 1987
American Mathematical Society