Corrigendum to: ``Compactifications of \(\mathbb{C}^ 3\). II'' (Q1318148)

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 \textit{Furushima}. The aim of this note is to show how to complete the proof.