Journal für die reine und angewandte Mathematik (Crelles Journal)

A smooth variety X over complex numbers is called Fano if its anticanonical divisor — Kx is ample. The purpose of this note is to collect some results on contractions of extremal rays (Mori theory) which are interesting from the point of describing Fano manifolds of dimension ^ 4. The theory has been successfully used in dimension 3, see [MM], and there is some hope that a similar approach may work somehow in higher dimensions. Furthermore, contractions of extremal rays of Fano manifolds can be… CONTINUE READING