| Co-Investigator(Kenkyū-buntansha) |
KONNO Kazuhiro Osaka University, Grad.Sch.of Sci., Associtate Professor, 大学院・理学研究科, 助教授 (10186869)
MORI Shigefumi Kyoto University, Research Institute of Math.Sci.Professor, 数理解析研究所, 教授 (00093328)
MUKAI Shigeru Nagoya University, Grad.Sch.of Math.Sci., Professor, 大学院・多元数理学研究科, 教授 (80115641)
KATO Kazuya University of Tokyo, Grad.Sch.of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (90111450)
NAKAMURA Iku Hokkaido University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (50022687)
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| Research Abstract |
We held also this year the Research Meeting which continues more than ten years :
"Hodge Theory Log Geometry Degenerations" October 12-16, 1998, Izumigo, Yatsugatake, Kitakoma-gun. Yamanashi, Organizers : Masaniri Asakura, Tatsuya Arakawa, Sampei Usui.
The topics of this year is as in the title. There were 16 expositions on this topics and there were stimulating discussions among the participants.
We held the following mini-workshop. All participants exposed their research results an4 had stimulating discussions among them : "Hodge Theory and Algebraic Geometry", January 28-31, 1999, Edel Sasayuri, Yatiyo-cho, Tka-gun, Hyogo, Organizer : Sampei Usui.
As in the last year, we had communications with the local people including high school students in leisure time. Both of us were satisfied with these communications.
Each research result is as follows : Sampei Usui and Kazuya Kato worked together and succeeded to construct (partial) compactifications of arithmetic quotients of classifying space
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s of Hodge structures with arbitrary Hodge types. This is a generalization of toroidal compactifications by Mumford et al. for Hermitian symmetric domains. We are preparing the paper. Kawamata investigated the deformations of canonical singularities and the extendability of pluri-canonical forms. Mukai made an exposition on polarized K3 surfaces in Euroconference in 1998. Mori made an exposition under the title of Rational curves on algebraic varieties and K Kato made an exposition under the title of Bloch Conjecture and p-adic epsilon elements in the Final Taniguchi Symposium in Nara, December 1998. Usui made an exposition under the title of Logarithmic Hodge structures and their classifying spaces and Masahiko Saito made an exposition under the title of Prepotentials of Yukawa couplings of certain Calabi-Yau 3-folds in NATO Advanced Study Institute in Banif, June 1998. Konno succeeded to solve 1-2-3 Conjecture of Reid completely. Ashikaga and Arakawa worked together and solved the Morsifications for hyper-elliptic pencils. Usa introduced and investigated the notion of geometric shells.
The other research results are found in the list of references on the next pages. Less
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