×

zbMATH — the first resource for mathematics

Some remarks about 1-convex manifolds on which all holomorphic line bundles are trivial. (English) Zbl 1111.32007
The author gives an abridged proof of an example in his paper [Rev. Roum. Math. Pures Appl. 43, No. 1–2, 97–104 (1998; Zbl 0932.32018)] of an 1-convex threefold on which every holomorphic line bundle is trivial. He points out several mistakes in the paper by Vo Van Tan [Bull. Sci. Math. 129, No. 6, 501–522 (2005; Zbl 1083.32010)] on related topics.

MSC:
32E05 Holomorphically convex complex spaces, reduction theory
32J05 Compactification of analytic spaces
32L20 Vanishing theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alessandrini, L.; Bassanelli, G., Transforms of currents by modifications and 1-convex manifolds, Osaka J. math., 40, 3, 717-740, (2003) · Zbl 1034.32009
[2] Ceresa, G.; Collino, A., Some remarks on algebraic equivalence of cycles, Pacific J. math., 105, 285-290, (1983) · Zbl 0542.14002
[3] Colţoiu, M., On 1-convex manifolds with 1-dimensional exceptional set, Rev. roumaine math. pures appl., 43, 97-104, (1998) · Zbl 0932.32018
[4] Grauert, H.; Riemenschneider, O., Kähler mannigfaltigkeiten mit hyper-q-konnvexen rand, (), 61-79
[5] Hamm, H.A.; Lê, D.T., Rectified homotopical depth and Grothendieck conjectures, Progress in math., vol. 87, (1990), Birkhäuser · Zbl 0725.14016
[6] Karĉjauscas, G., A generalized Lefschetz theorem, Funct. anal. appl., 11, 312-313, (1977)
[7] H. Laufer, On \(C \mathbb{P}^1\) as exceptional set, in: Recent Developments in S.C.V., Ann. Math. Studies, Princeton, NJ, 1981, pp. 261-267
[8] Moishezon, B.G., On n-dimensional compact algebraic varieties with n algebraically independent meromorphic functions, Amer. math. soc. transl. 2, 63, 51-177, (1967) · Zbl 0186.26204
[9] Mori, S., Flip theorem and existence of minimal models for 3-folds, J. amer. math. soc., 1, 117-253, (1988) · Zbl 0649.14023
[10] Nakano, S., On the inverse of a monoidal transformation, Publ. RIMS Kyoto univ., Publ. RIMS Kyoto univ., 7, 637-644, (1972) · Zbl 0234.32019
[11] Peternell, T., On strongly pseudoconvex Kähler manifolds, Invent. math., 70, 2, 157-168, (1982/1983) · Zbl 0505.32023
[12] G.K. Sankaran, Math. Reviews, 2142895
[13] Vâjâitu, V., On embeddable 1-convex spaces, Osaka J. math., 38, 287-294, (2001) · Zbl 0982.32010
[14] Vo Van Tan, On the quasiprojectivity of compactifiable strongly pseudoconvex manifolds, Bull. sci. math., 129, 501-522, (2005) · Zbl 1083.32010
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.