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，该会议持续了十多年：“ Hodge理论日志几何变化” 1998年10月12日至16日，Izumigo，Yatsugatake，Kitakoma-Gun。 Yamanashi，组织者：Masaniri Asakura，Tatsuya Arakawa，Sampei Usui。今年的主题与标题一样。关于这个主题有16个论述，参与者之间进行了令人兴奋的讨论。我们举行了以下小型工作室。所有参与者都揭示了他们的研究结果AN4在其中进行了刺激的讨论：“霍奇理论和代数几何形状”，1999年1月28日至31日，Edel Sasayuri，Yatiyo-Cho，Tka-gun，Tka-gun，whoogo，noogo，noogo，组织者，组织者：Sampei usui.As as sampei usui.as在上一年中，我们与当地的学生（包括当地的学生在内的时间，都有在包括莱斯学生在内的高级学生。我们俩都对这些通信感到满意。每个研究结果如下：Sampei Usui和Kazuya Kato共同努力，成功地构建了（部分）对分类空间的算术引用的（部分）压缩……更多的Hodge结构具有任意Hodge类型的霍奇结构。这是Mumford等人对环形压缩的概括。对于Hermitian对称域。我们正在准备纸。川塔（Kawamata）研究了规范奇异性的变形和折叠形式的扩展性。穆凯（Mukai）在1998年的欧洲会议中对两极分化的K3表面进行了说明。分类空间和Masahiko Saito在1998年6月在Banif的北约高级研究所的某些Calabi-Yau的Yukawa耦合的标题下进行了展览。Konno成功地解决了Reid的1-2-3猜想。 Ashikaga和Arakawa共同努力，解决了高纤维化铅笔的重视。美国引入并研究了几何壳的概念。其他研究结果在下一页的参考列表中找到。较少的