Nakamura, Iku Moishezon-Fano threefolds of index three. (English) Zbl 0816.14014 J. Fac. Sci., Univ. Tokyo, Sect. I A 40, No. 2, 429-449 (1993). The author studies the Moishezon threefolds \(X\) with \(h^ 1 (X, {\mathcal O}_ X) = 0\), whose canonical bundle is \(K_ X = - nL\) \((n \geq 3)\) for some line bundle \(L\) with \(h^ 0 (X,L) \geq 2\). In particular he proves that:(i) if \(n = 4\), \(X\) is isomorphic to \(\mathbb{P}^ 3\); (ii) if \(n = 3\) and \(L\) has no fixed components, \(X\) is isomorphic either to a quadric or to a \(\mathbb{P}^ 2\)-bundle over \(\mathbb{P}^ 1\).The situation differs from the analogous algebraic case: it is known that the unique projective Fano threefold of index 3 is, up to isomorphism, the quadratic hypersurface of \(\mathbb{P}^ 4\). Reviewer: L.Picco Botta (Torino) MSC: 14J30 \(3\)-folds 14J45 Fano varieties 32J17 Compact complex \(3\)-folds Keywords:Moishezon threefolds; canonical bundle PDFBibTeX XMLCite \textit{I. Nakamura}, J. Fac. Sci., Univ. Tokyo, Sect. I A 40, No. 2, 429--449 (1993; Zbl 0816.14014)