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Analysis of varieties – the work of Dr. Yoichi Miyaoka. (Japanese) Zbl 0759.14026
Yoichi Miyaoka won the prize of the Mathematical Society of Japan in spring, 1989. This report is an introduction of his main results in celebration of his receiving the prize. The author explains Y. Miyaoka’s contributions to the classification theory of algebraic surfaces, and to the proof of the existence of minimal models for 3-folds. This report is finished by the famous Miyaoka-Yau inequality and the possibility of its applications to the arithmetic geometry.
##### MSC:
 14J10 Families, moduli, classification: algebraic theory 01A70 Biographies, obituaries, personalia, bibliographies 14E30 Minimal model program (Mori theory, extremal rays) 14J30 $$3$$-folds 14-03 History of algebraic geometry