an:03865464
Zbl 0544.14009
Kawamata, Yujiro
The cone of curves of algebraic varieties
EN
Ann. Math. (2) 119, 603-633 (1984).
00283940
1984
j
14E30 14J30
cone of curves; vanishing theorem; minimal models of algebraic varieties; contraction theorem
In this paper two of the four steps are proved toward the theory of minimal models of algebraic varieties according to the program of M. Reid; we have proved: (1) the cone theorem; (2) the contraction theorem, and there remains: (3) the flip conjecture; (4) the induction conjecture. - \textit{J. Koll??r} [ibid. 120, 1-5 (1984; see the following review)] proved the discreteness of the extremal rays and completed the picture of the cone. We note here that our theorems are easily generalised to the relative case starting from a projective morphism \(f:X\to S\) instead of a projective variety X.
Zbl 0544.14008; Zbl 0544.14010