The finite generation theorem is a major achievement of modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an al

Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model progra

Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in