Moišezon spaces and almost positive coherent sheaves
The main result in this paper is Theorem 2.4: Let X be a compact reduced irreducible normal complex space. X is Moishezon precisely if there exists a (torsion free) coherent sheaf F on X which is almost positive and globally generated. In the case of complex surfaces, the author is able to eliminate the phrase ''globally generated'' from this statement (Theorem 3.3); i.e., he verifies in the affirmative, in the case of dimension 2, Grauert and Riemenschneider's conjectured characterization of Moishezon spaces. The key fact the author uses in the proof of Theorem 2.4 is that if L is a holomorphic line bundle on a compact analytic space \(X^ n\) such that \(c_ 1(L^ n)\) is positive and such that some power of L is globally generated, then X is Moishezon. The author proves this key fact via a straightforward argument involving numerical inequalities. These inequalities yield that the transcendence degree of the field of meromorphic functions on X is equal to n.
scientific article; zbMATH DE number 4000381
scientific article