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Non-projective compactifications of \(\mathbb{C}^ 3\). I. (English) Zbl 0886.32021
The author determines the singular Fano compactifications \((V,A)\) of \({\mathbb{C}}^{3}\) with index \(r=2\). In fact, it is shown that \((V,A) \cong (V_{4},H_{4})\), where \(V_{4}\) is a complete intersection of two quadrics in \({\mathbb{P}}^{5}\) with exactly one small Gorestein singularity \(p\), and \(H_{4}\) is a non-normal hyperplane section of \(V_{4}\) which is a non-normal cone over a nodal curve in \({\mathbb{P}}^{3}\) of degree \(4\).

MSC:
32J05 Compactification of analytic spaces
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