Elementary contractions of algebraic 3-folds. (English) Zbl 0542.14007

Kawamata, Yujiro

Ann. Math. (2) 119, 95-110 (1984).

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).

MSC:

14E30	Minimal model program (Mori theory, extremal rays)
14E05	Rational and birational maps
14J30	\(3\)-folds

Keywords:

minimal models of algebraic 3-folds

Citations:

Zbl 0544.14009