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Algebraic Geometry and Hodge Theory

代数几何和霍奇理论

基本信息

批准号：
08304002
负责人：
USUI Sampei
金额：
$ 3.9万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304002/
关键词：
Hodge theory Logarithmic geometry Algebraic varieties Pluri-canonical forms K3 surfaces Canonical curves Calabi-Yau manifolds Morsification Hodge 理論 Log 幾何学多重標準形成 K3曲面 calabi-yau多様体 Hodge構造の分類空間部分コンパクト化藤田の自由予想 Calabi-Yau

项目摘要

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

我们还举行了今年的研究会议，继续超过十年：“霍奇理论日志几何退化”1998年10月12日至16日，泉后，八岳，北驹郡。主办单位：朝仓正里、荒川达也、三井三平。今年的主题如标题所示。我们举办了16场关于这一主题的研讨会，与会者进行了热烈的讨论。所有参加者都展示了自己的研究成果，并进行了热烈的讨论。“霍奇理论和代数几何”，1999年1月28日至31日，兵库县德川郡八代代町，Edel Sasayuri，组织者：Sampei Yaoi。我们对这些交流都很满意，各自的研究成果如下：Sampei Yanji和Kazuya Kato合作成功地构造了分类空间的算术行列式的（部分）紧化 ...更多信息的任意Hodge类型的Hodge结构。这是Mumford等人对Hermitian对称域的环面紧化的推广。我们正在准备论文。川又研究了正则奇点的变形和多正则形式的可拓性。Mukai在1998年的欧洲会议上对极化K3曲面进行了阐述。森提出了一个博览会的标题下理性曲线的代数品种和加藤K提出了一个博览会的标题下布洛赫猜想和p-进元的最后谷口研讨会在奈良，1998年12月。1998年6月，在位于巴尼夫的北约高级研究所，齐藤雅彦以对数霍奇结构及其分类空间为题进行了一次阐述，并以汤川耦合的某些卡-丘3倍的Prepotential为题进行了阐述。Konno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Morsifications。美国提出并研究了几何壳的概念，其他研究成果见下页的参考文献。少