Algebraic Geometry and Hodge Theory

今年我们还举行了持续十多年的研究会议：“霍奇理论原木几何退化”，1998年10月12-16日，出水、山竹、北马-枪。山梨，主办方：浅仓正郎，荒川达也，宇三平。今年的主题如标题所示。就这一主题进行了16次阐述，与会者进行了激动人心的讨论。我们举办了以下小型研讨会。所有参与者都展示了他们的研究成果，其中4人进行了激动人心的讨论：1999年1月28-31日的《霍奇理论与代数几何》，Edel Sasayuri，Yatiyo-cho，Tka-Gun，兵库，组织者：Sampeu Usu.和去年一样，我们在闲暇时间与包括高中生在内的当地民众进行了交流。各自的研究成果如下：上井三培和加藤和也合作，成功地构造了分类空间…的算术商的(部分)紧化S对具有任意霍奇类型的霍奇结构的研究较多。这是Mumford等人对环形紧凑化的推广。用于厄米特对称域。我们正在准备这篇论文。Kawamata研究了正则奇点的变形和多正则形式的可扩性。Mukai在1998年的欧洲会议上发表了关于极化K3表面的论述。Mori以代数簇上的有理曲线为题进行了论述，K Kato在1998年12月于奈良举行的谷口研讨会最后一次会议上以Bloch猜想和p-进epsilon元为题进行了论述。Usui和Masahiko Saito分别以对数Hodge结构及其分类空间和Masahiko Saito在1998年6月在巴尼夫的北约高级研究所发表的关于某些Calabi-Yau三折的Yukawa耦合的前势的标题进行了阐述。Konno完全解决了Reid的1-2-3猜想。Ashikaga和Arakawa一起工作，解决了超椭圆铅笔的莫里西化问题。美国介绍并研究了几何壳的概念。其他研究成果可在下一页的参考文献列表中找到。较少

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