The purpose of this ebook is to introduce the reader to the geometric thought of algebraic forms, 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 no touching on different books, comparable to textbooks on commutative algebra. The reader is just anticipated to understand the definition of Noetherin earrings and the assertion of the Hilbert foundation theorem. the hot chapters 1, 2, and 10 were accelerated. specifically, the exposition of D-dimension idea, even if shorter, is extra entire than within the previous model. despite the fact that, to maintain the ebook of achievable dimension, the latter elements of Chapters 6, nine, and eleven were got rid of. I thank Mr. A. Sevenster for encouraging me to write down this re-creation, and Professors ok. ok. Kubota in Kentucky and P. M. H. Wilson in Cam bridge for his or her cautious and significant analyzing of the English manuscripts and typescripts. I held seminars in response to the cloth during this ebook on the college of Tokyo, the place various precious reviews and proposals got via scholars Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.

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