Zariski-decomposition and Abundance

Dr. Noboru Nakayama, the author of this book, studies the birational\nclassification of algebraic varieties and of compact complex manifolds. This\nbook is a collection of his works on the numerical aspects of divisors of\nalgebraic varieties. The notion of Zariski-decomposition introduced by Oscar\nZariski is a powerful tool in the study of open surfaces. In the higher\ndimensional generalization, we encounter interesting phenomena on the numerical\naspects of divisors. The author treats the higher dimensional\nZariski-decomposition systematically. The abundance conjecture predicts that the\nnumerical Kodaira dimension of a minimal variety coincides with the usual\nKodaira dimension. The Kodaira dimension is an invariant of the canonical\ndivisor of a variety. The numerical analogue used to be defined only for nef\ndivisors, but it is now extended to arbitrary divisors in this book. Explained\nin details are many important results on the numerical Kodaira dimension related\nto the abundance, to the addition theorem for fiber spaces, and to the\ndeformation invariance.