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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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