Elementary contractions of algebraic 3-folds (Q795110)

This paper gives proofs of some steps toward the theory of minimal models of algebraic 3-folds. Let X be an algebraic 3-fold which admits some mild singularities. Then the theorems are: (1) The closed cone of curves on X is generated by extremal rays in the half space \(K_ X<0\). (2) An extremal ray can be contracted by a morphism from X. - The proof uses a result previously obtained by the author in the paper ''On the finiteness of generators of a pluri-canonical ring for a 3-fold of general type'' (Am. J. Math.; to appear). A generalization to higher dimensional case is obtained in Ann. Math., II. Ser. 119, 603-633 (1984; Zbl 0544.14009).