By S. Iitaka

The purpose of this ebook is to introduce the reader to the geometric conception of algebraic types, particularly to the birational geometry of algebraic kinds. This quantity grew out of the author's e-book in eastern released in three volumes through Iwanami, Tokyo, in 1977. whereas penning this English model, the writer has attempted to arrange and rewrite the unique fabric in order that even rookies can learn it simply with out touching on different books, corresponding to textbooks on commutative algebra. The reader is simply anticipated to understand the definition of Noetherin earrings and the assertion of the Hilbert foundation theorem. the hot chapters 1, 2, and 10 were increased. particularly, the exposition of D-dimension concept, even though shorter, is extra entire than within the outdated model. in spite of the fact that, to maintain the e-book of achievable dimension, the latter components of Chapters 6, nine, and eleven were got rid of. I thank Mr. A. Sevenster for encouraging me to put in writing this new edition, and Professors okay. okay. Kubota in Kentucky and P. M. H. Wilson in Cam bridge for his or her cautious and demanding analyzing of the English manuscripts and typescripts. I held seminars according to the cloth during this ebook on the college of Tokyo, the place plenty of useful reviews and recommendations got by means of scholars Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.