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Corrigendum to: “Compactifications of \(\mathbb{C}^ 3\). II”. (English) Zbl 0799.14021
In the paper cited in the title [ibid. 283, No. 1, 121-137 (1989; Zbl 0671.14020)], I studied algebraic compactifications \(X\) of \(\mathbb{C}^ 3\) with second Betti number 1 (which are necessarily Fano manifolds) and nonnormal divisor at infinity \(Y\). The main result was the following:
If the index of \(X\) is 1, then its genus is 12, in particular \(X\) is rational with \(b_ 3 = 0\).
In the proof however there is a gap as pointed out by Furushima. The aim of this note is to show how to complete the proof.
MSC:
14J30 \(3\)-folds
32J05 Compactification of analytic spaces
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References:
[1] Barthel, G., Kaup, L.: Topologie des espaces complexes compactes singulieres. Montreal Lecture Notes80 (1982) · Zbl 0494.32011
[2] Furushima, M.: The complete classification of compactifications of C3 which are projective manifolds with the second Betti number one. Preprint 1992
[3] Peternell, T.: Compactifications of ?3. II. Math. Ann.283, 121-137 (1989) · Zbl 0671.14020
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