Algebraic structures on certain 3-folds
This paper is the second part of a previous one [the author, Manuscr. Math. 50, 397-428 (1985; Zbl 0573.32027)] and is devoted to complete the proof of the following theorem (filling a gap pointed out by the author in an ''addendum'' to the previous paper). Let \(X\) be a Moishezon 3-fold which is topologically isomorphic to \(\mathbb{P}^3\); then \(X\) is biholomorphic to \(\mathbb{P}^3\). The analogous statement for the smooth 3- dimensional quadric is proved simultaneously. Let \(X\) be as above; assuming that the theorem is not true, the author takes a modification \(\pi : \hat X\to X,\) which is a finite sequence of blow-ups with smooth centers, such that \(\hat X\) is projective. Then he studies the extremal rays on \(\hat X\) and the corresponding modifications according to Mori's theory [\textit{S. Mori}, Ann. Math., II. Ser. 116, 133-176 (1982; Zbl 0557.14021)] finding a contradiction, after a case by case analysis.
characterization of complex projective 3-space
scientific article; zbMATH DE number 3955113