Algebraic Geometry and Hodge Theory

我们今年还举行了持续了十多年的研究会议：“Hodge理论测井几何退化”，1998年10月12日至16日，出云乡，矢竹县，北间县。组织者：浅仓正理、荒川达也、臼井三平。今年的主题如标题所示。围绕这一主题的展览有16个，与会者之间进行了热烈的讨论。我们举办了以下小型研讨会。所有参与者都公开了他们的研究成果，并进行了激烈的讨论：“Hodge理论和代数几何”，1999年1月28-31日，Edel Sasayuri, Yatiyo-cho, Tka-gun，兵库县，组织者：臼井三平。和去年一样，我们在业余时间和当地的高中生进行交流。我们双方都对这些交流感到满意。每项研究成果如下：Sampei Usui和Kazuya Kato合作，成功构造了分类空间算术商的（部分）紧化。这是Mumford等人对厄米对称域的环面紧化的推广。我们正在准备论文。Kawamata研究了典型奇点的变形和多典型形式的可扩展性。1998年，向井在欧洲会议上对极化K3曲面作了阐述。1998年12月，Mori在奈良的谷口研讨会上以“代数变数上的有理曲线”为题作了论述，K Kato以“布洛赫猜想和p进元”为题作了论述。臼井作了对数Hodge结构及其分类空间的论述，Masahiko Saito作了某些Calabi-Yau 3-fold的Yukawa耦合的预势的论述，1998年6月在Banif的NATO高级研究所。Konno成功地完全解决了Reid的1-2-3猜想。足利和荒川一起解决了超椭圆铅笔的morsitification问题。美国引入并研究了几何壳的概念。其他的研究结果在下一页的参考文献列表中找到。少

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 … More 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