Über exzeptionelle Mengen
A linear fibre space V over a complex space X is said to be weakly negative if the zero section is exceptional (i.e., can be contracted to a point). If Y is a subspace of X, the normal bundle to Y is the linear (fibre) space \(N_ Y\) dual to the sheaf \(I/I^ 2\), I being the ideal sheaf of Y. \textit{H. Grauert} [Math. Ann. 146, 331-368 (1962; Zbl 0173.330)] proved a famous theorem to the effect that Y is exceptional if \(N_ Y\) is weakly negative. In this paper (and subsequent correction) it is proved, conversely, that if Y' is an exceptional set, then there is a subspace Y, with \(Y_{red}=Y'\), having weakly negative normal bundle. As a corollary, the author proves the converse of a result of \textit{V. Ancona} [Trans. Am. Math. Soc. 215, 45-61 (1976; Zbl 0319.32015)] stating that X is a Moishezon space if there is a weakly negative linear fibre space V on X with all fibres of dimension \(>0\). - Relative versions of the main theorem [which was also proved by \textit{L. Ancona} and \textit{G. Tomassini}, ''Modifications analytiques'', Lect. Notes Math. 943 (1982; Zbl 0498.32006), independently] are given. The proof of theorem 3 is incomprehensible to the reviewer.
scientific article; zbMATH DE number 3869716