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Higher Dimensional Algebraic Varieties

高维代数簇

基本信息

批准号：
04044081
负责人：
MORI Shigefumi
金额：
$ 8.06万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for international Scientific Research
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04044081/
关键词：
Minimal model flip Fano variety Shafarevich map Hodge theory Calabi-Yau variety vector bundle Teichmueller space 極小モデル理論基本群フェルリンデ公式射影空間

项目摘要

The central purpose of this project was to study higher dimensional algebraic varieties, specially from the viewpoint of external rays. We aimed at the study of the various aspects of algebraic varieties by supporting 20 Japanese mathematicians participating in the algebraic geometry year at MSRI (92/93) and RGI summer institute 93. The project also partially supported Fulton, Looijenga and Matsuki.Kollar, Miyaoka and Mori have been jointly studying the deformation of algebraic curves on an algebraic variety. Kollar has combined the deformation method with fundamental groups to construct the Shafarevich maps in his recent study of algebraic varieties with big algebraic fundamental groups. They also generalized Kawamata's boundedness theorem of Q-Fano 3-folds to arbitrary Picard number case.As for 3-dimensional minimal model theory, Matsuki generalized Kawamata's important abundance theorem to the log case jointly with S. Keel and J. McKernan. Kawamata proved the semi-stable minimal model theory in positive characteristics. Mori proved Reid's general elephant conjecture for arbitrary 3-dimensional flipping contractions.Special varieties are also studied : Oguiso studied on fiber space structures of Calabi-Yau 3-folds, Mukai on Gorenstein Fano 3-folds and Konno on special canonical mappings of surfaces of general type. Cho and Miyaoka are working on the characterization of projective spaces.A few from other aspects : Kyoji Saito has expressed Teichmuller spaces as real semi-algebraic affine schemes defined over the ring of integers. Usui constructed certain partial compactifications of the arithmetic quotients of the classifying spaces of Hodge structures, and Masahiko Saito studied Neron models using canonical extensions of Hodge structures.

该项目的中心目的是研究高维代数变量，特别是从外部射线的角度。我们旨在通过支持20名日本数学家参加MSRI（92/93）和RGI暑期研究所93的代数几何年，研究代数变体的各个方面。该项目还部分支持了Fulton， Looijenga和Matsuki。Kollar， Miyaoka和Mori一直在共同研究代数曲线在代数变量上的变形。Kollar在最近对具有大代数基本群的代数变异的研究中，将变形方法与基本群相结合，构造了Shafarevich映射。他们还将Q-Fano 3-fold的Kawamata有界定理推广到任意Picard数的情况。在三维极小模型理论方面，Matsuki与S. Keel和J. McKernan共同将Kawamata的重要丰度定理推广到对数情况。Kawamata在正特征下证明了半稳定极小模型理论。Mori对任意三维翻转收缩证明了Reid的一般大象猜想。此外，Oguiso研究了Calabi-Yau 3-fold的纤维空间结构，Mukai研究了Gorenstein Fano 3-fold， Konno研究了一般类型曲面的特殊正则映射。Cho和Miyaoka正在研究投影空间的特征。从其他方面：Kyoji Saito将Teichmuller空间表示为定义在整数环上的实半代数仿射格式。Usui构造了Hodge结构分类空间的算术商的部分紧化，Masahiko Saito利用Hodge结构的正则扩展研究了Neron模型。