| Co-Investigator(Kenkyū-buntansha) |
HAYAKAWA Takayuki Fac. of Sci., Kanazawa Univ., 理学部, 助手 (20198823)
YOKOGAWA Koji Fac. of Sci., Osaka Univ., 理学部, 助手 (40240189)
MUKAI Shigeru Fac. of Sci., Nagoya Univ., 理学部, 教授 (80115641)
TSUNODA Shuichiro Fac. of Sci., Osaka Univ., 理学部, 助教授 (60144424)
MORIWAKI Atsushi Fac. of Sci., Kyoto Univ., 理学部, 助手 (70191062)
SUGIE Toru Fac. of Education, Shiga Univ., 教育学部, 助教授 (90135509)
MARUYAMA Masaki Fac. of Sci., Kyoto Univ., 理学部, 教授 (50025459)
SAITO Masahiko Fac. of Sci., Kyoto Univ., 理学部, 助教授 (80183044)
USUI Sampei College of General Education, Osaka Univ., 教養部, 教授 (90117002)
KONNO Kazuhiro College of General Education, Kyushu Univ., 教養部, 助教授 (10186869)
UENO Kenji Fac. of Sci., Kyoto Univ., 理学部, 教授 (40011655)
SAITO Morihiko RIMS, Kyoto Univ., 数理解析研究所, 助教授 (10186968)
SAITO Kyoji RIMS, Kyoto Univ., 数理解析研究所, 教授 (20012445)
KOBAYASHI Masanori Fac. of Sci., Tokyo Inst. of Tech., 理学部, 助手 (60234845)
FUJITA Takao Fac. of Sci., Tokyo Inst. of Tech., 理学部, 教授 (40092324)
TSUJI Hajime Fac. of Sci., Tokyo Inst. of Tech., 理学部, 助教授 (30172000)
MIYAOKA Yoichi RIMS, Kyoto Univ., 数理解析研究所, 教授 (50101077)
OGUISO Keiji Fac. of Sci., Ochanomizu Univ., 理学部, 講師 (40224133)
NAKAYAMA Noboru Dept. of Math. Sci., The Univ. of Tokyo, 大学院・数理科学研究科, 助教授 (10189079)
KAWAMATA Yujiro Dept. of Math. Sci., The Univ. of Tokyo, 大学院・数理科学研究科, 教授 (90126037)
CLEMENS Herb Dept. of Math., Univ. of Utah, 教授
KOLLAR Janos Dept. of Math., Univ. of Utah, 教授
ISHIDA Masanori Fac. of Sci., Tohoku Univ., 理学部, 助教授 (30124548)
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| Research Abstract |
The central purpose of this project was to study higher dimensional algebraic varieties, specially from the viewpoint of external rays. We aimed at the study of the various aspects of algebraic varieties by supporting 20 Japanese mathematicians participating in the algebraic geometry year at MSRI (92/93) and RGI summer institute 93. The project also partially supported Fulton, Looijenga and Matsuki.
Kollar, Miyaoka and Mori have been jointly studying the deformation of algebraic curves on an algebraic variety. Kollar has combined the deformation method with fundamental groups to construct the Shafarevich maps in his recent study of algebraic varieties with big algebraic fundamental groups. They also generalized Kawamata's boundedness theorem of Q-Fano 3-folds to arbitrary Picard number case.
As for 3-dimensional minimal model theory, Matsuki generalized Kawamata's important abundance theorem to the log case jointly with S. Keel and J. McKernan. Kawamata proved the semi-stable minimal model theory in positive characteristics. Mori proved Reid's general elephant conjecture for arbitrary 3-dimensional flipping contractions.
Special varieties are also studied : Oguiso studied on fiber space structures of Calabi-Yau 3-folds, Mukai on Gorenstein Fano 3-folds and Konno on special canonical mappings of surfaces of general type. Cho and Miyaoka are working on the characterization of projective spaces.
A few from other aspects : Kyoji Saito has expressed Teichmuller spaces as real semi-algebraic affine schemes defined over the ring of integers. Usui constructed certain partial compactifications of the arithmetic quotients of the classifying spaces of Hodge structures, and Masahiko Saito studied Neron models using canonical extensions of Hodge structures.
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