The Castelnuovo--Enriques contraction theorem for arbitrary dimension

B. G. Moishezon

Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 917-966

Résumé

In the present article we show that the $n$-dimensional generalization of the Castelnuovo–Enriques theorem concerning exceptional curves of the first kind on algebraic surfaces is valid in the category of minischemes over any algebraically closed field. The following result is deduced as a corollary: for every $n$-dimensional compact complex manifold $Y$ with $n$ algebraically independent meromorphic functions there exists a nonsingular minischeme $V$ over the complex field such that the complex manifold $V_\mathbf C$ canonically corresponding to $V$ coincides with $Y^*$.