The Levi problem for the product space of a Stein space and a compact Riemann surface

Kiyoshi WATANABE

doi:10.2969/jmsj/02840605

Kiyoshi WATANABE

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JOURNAL FREE ACCESS

1976 Volume 28 Issue 4 Pages 605-610

DOI https://doi.org/10.2969/jmsj/02840605

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Published: 1976 Received: April 14, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Andreotti and R. Narasimhan, Oka's heftungslemma and the Levi problem for complex spaces, Trans. Amer. Math. Soc., 111 (1964), 345-366.
2) A. Fujiki, On the blowing down of analytic spaces, Publ. Res. Inst. Math. Sci., 10 (1975), 473-507.
3) H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
4) H. Hironaka, Bimeromorphic smoothing of a complex-analytic space, Preprint, University of Warwick, 1970.
5) P. Lelong, Domaines convexes par rapport aux fonctions plurisousharmoniques, J. Analyse Math., 2 (1952), 178-208.
6) Y. Matsugu, The Levi problem for a product manifold, Pacific J. Math., 46 (1973), 231-233.
7) S. Nakano, Vanishing theorems for weakly 1-complete manifolds, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, 169-179.
8) R. Narasimhan, The Levi problem for complex spaces, Math. Ann., 142 (1961), 355-365.
9) K. Oka, Sur les fonctions analytiques de plusieurs variables: IX Domains finis sans point critique intérieur, Japan. J. Math., 23 (1953), 97-155.
10) K. Stein, Überlagerung holomorph-vollständiger komplex Raume, Arch. Math., 7 (1956), 354-361.
11) S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, New Jersey, 1964.
12) K. Watanabe, The Levi problem for the product manifold of an open Riemann surface and a compact Riemann surface, Men. Fac. Sci. Kyushu Univ. Ser. A., 29 (1975), 211-222.

Right : [1] A. Andreotti and R. Narasimhan, Oka's heftungslemma and the Levi problem for complex spaces, Trans. Amer. Math. Soc., 111 (1964), 345-366.
[2] A. Fujiki, On the blowing down of analytic spaces, Publ. Res. Inst. Math. Sci., 10 (1975), 473-507.
[3] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
[4] H. Hironaka, Bimeromorphic smoothing of a complex-analytic space, Preprint, University of Warwick, 1970.
[5] P. Lelong, Domaines convexes par rapport aux fonctions plurisousharmoniques, J. Analyse Math., 2 (1952), 178-208.
[6] Y. Matsugu, The Levi problem for a product manifold, Pacific J. Math., 46 (1973), 231-233.
[7] S. Nakano, Vanishing theorems for weakly 1-complete manifolds, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, 169-179.
[8] R. Narasimhan, The Levi problem for complex spaces, Math. Ann., 142 (1961), 355-365.
[9] K. Oka, Sur les fonctions analytiques de plusieurs variables: IX Domains finis sans point critique intérieur, Japan. J. Math., 23 (1953), 97-155.
[10] K. Stein, Überlagerung holomorph-vollständiger komplex Räume, Arch. Math., 7 (1956), 354-361.
[11] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, New Jersey, 1964.
[12] K. Watanabe, The Levi problem for the product manifold of an open Riemann surface and a compact Riemann surface, Men. Fac. Sci. Kyushu Univ. Ser. A., 29 (1975), 211-222.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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