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

今年我们还举办了持续十多年的研究会议：“Hodge理论测井几何退化”，1998年10月12日至16日，山梨县八岳泉乡，组织者：朝仓正入、荒川达也、臼井三平。今年的主题如标题所示，共有16个主题的阐述，与会人员进行了热烈的讨论。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，并进行了热烈的讨论：“Hodge理论和代数几何”，1999年1月28日至31日，Edel Sasayuri，Yatiyo-cho，Tka-gun，Hyogo，主办方：臼井三平。与去年一样，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，我们双方都对这些交流感到满意。各项研究结果如下： Sampei Usui 和 Kazuya Kato 共同构建了具有任意 Hodge 类型的分类空间算术商的（部分）紧缩，这是 Mumford 等人对 Hermitian 对称域的环形紧缩的推广。 Kawamata 正在准备论文，研究了规范奇点的变形和 Mukai 提出的多规范形式的可扩展性。 1998年欧洲会议上关于极化K3曲面的阐述。Mori在代数簇上的有理曲线的标题下进行了阐述，K Kato在奈良谷口最终研讨会上以布洛赫猜想和p-adic epsilon元素的标题进行了阐述， 1998年12月，臼井作了题为“对数Hodge结构及其分类空间”的阐述，斋藤正彦作了1998 年 6 月，在巴尼夫的北约高级研究所，以“某些 Calabi-Yau 3 倍的 Yukawa 偶合的预势”为题发表了论文。绀野成功地解决了足利和荒川的 1-2-3 猜想。超椭圆铅笔的变形。美国介绍并研究了几何壳的概念。其他研究结果可在下页的参考文献列表中找到。