By S. Iitaka

The purpose of this ebook is to introduce the reader to the geometric idea of algebraic types, particularly to the birational geometry of algebraic forms. This quantity grew out of the author's ebook in jap released in three volumes by means of Iwanami, Tokyo, in 1977. whereas scripting this English model, the writer has attempted to arrange and rewrite the unique fabric in order that even novices can learn it simply with no bearing on different books, corresponding to textbooks on commutative algebra. The reader is simply anticipated to grasp the definition of Noetherin jewelry and the assertion of the Hilbert foundation theorem. the recent chapters 1, 2, and 10 were multiplied. specifically, the exposition of D-dimension idea, even supposing shorter, is extra whole than within the outdated model. in spite of the fact that, to maintain the publication of workable measurement, 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 re-creation, and Professors okay. ok. Kubota in Kentucky and P. M. H. Wilson in CamĀ bridge for his or her cautious and important interpreting of the English manuscripts and typescripts. I held seminars in response to the fabric during this e-book on the college of Tokyo, the place various important reviews and proposals got by way of scholars Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.