标题： 3-流形的显式双有理几何，前言 显示英文标题

标题： Explicit birational geometry of 3-folds, Foreword

摘要： 这是书籍《三维流形的显式双有理几何》的序言，由A. Corti和M. Reid编辑，剑桥大学出版社2000年6月出版，ISBN：0 521 63641 8，其中包含K. Altmann、A. Corti、A.R. Iano-Fletcher、J. Kollár、A.V. Pukhlikov和M. Reid的文章。 代数几何在过去20年中的主要成就之一是Mori和其他人的工作，将极小模型和Enriques--Kodaira分类扩展到三维流形。 本书是一套综合论文，围绕Mori理论在双有理几何中的应用展开。其中四篇论文（Pukhlikov、Fletcher、Corti以及Corti、Pukhlikov和Reid的长篇联合论文）详细阐述了Fano三维流形的双有理刚性理论；这些贡献首次针对Fano代数的一个代表性类，即加权射影空间中的三维超曲面，并包括一个吸引人的介绍性内容和大量特殊案例的详细计算。 显示英文摘要

摘要： This is the Foreword to the book ``Explicit birational geometry of 3-folds'', edited by A. Corti and M. Reid, CUP Jun 2000, ISBN: 0 521 63641 8, with papers by K. Altmann, A. Corti, A.R. Iano-Fletcher, J. Koll\'ar, A.V. Pukhlikov and M. Reid. One of the main achievements of algebraic geometry over the last 20 years is the work of Mori and others extending minimal models and the Enriques--Kodaira classification to 3-folds. This book is an integrated suite of papers centred around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper Corti, Pukhlikov and Reid) work out in detail the theory of birational rigidity of Fano 3-folds; these contributions work for the first time with a representative class of Fano varieties, 3-fold hypersurfaces in weighted projective space, and include an attractive introductory treatment and a wealth of detailed computation of special cases.