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Torus embedding and fiber space

环面嵌入和光纤空间

基本信息

批准号：
16540025
负责人：
NAKAYAMA Noboru
金额：
$ 1.09万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540025/
关键词：
toric variery complex torus Hodge structure fiber space

项目摘要

In the research, the following four objects related to the theories of torus embedding and torus fibration were studied :1. Toric bundles; 2. Nearly smooth torus fibrations; 3. Varieties admitting non-trivial surjective endomorphisms; 4. Normal quartic surfaces and log del Pezzo surfaces.1. Constructions of toric bundles and description of divisors on them are given. Unfortunately, there was no significant progress toward constructing the theory of degenerations of tonic bundles.2. The local structure of a Kahler torus fibration is determined when the singular fibers have open neighborhoods whose universal covering space does not have any positive dimensional subvarieties. The global bimeromorphic equivalence classes of Kahler torus fibrations which have locally finite monodromies are described as elements of a certain cohomology group under a fixed variation of Hodge structure.3. By the theories of torus embedding and elliptic fibration, the classification of varieties admitting non-trivial surjective endomorphisms is done in the cases of nonsingular compact complex surfaces and nonsingular projective threefolds with non-negative Kodaira dimension (joint work with Yoshio Fujimoto).4. The classification of normal quartic surfaces with irrational singularities (joint work with Yuji Ishii) and that of log del Pezzo surfaces of index two are given by the ideas of separation of divisors and the elimination of a zero-dimensional subscheme, respectively.

本论文主要研究了以下四个与环面嵌入和环面纤维化理论相关的问题：1。Toric bundles; 2.近光滑环面纤维化; 3.变种承认非平凡满自同态; 4。正规四次曲面和log del Pezzo曲面。1.给出了复曲面丛的构造和其上因子的刻画。不幸的是，在构建强直性脊柱炎退化理论方面没有取得重大进展。当Kahler环面纤维化的奇异纤维具有开邻域且其泛覆盖空间不具有任何正维子簇时，确定了其局部结构。具有局部有限单值的Kahler环面纤维化的整体双半纯等价类被描述为在固定的Hodge结构变差下的某个上同调群的元素.利用环面嵌入理论和椭圆纤维化理论，在非奇异紧致复曲面和非奇异射影三重且具有非负科代拉维数的情况下，对包含非平凡满射自同态的簇进行了分类（与Yoshio Fujimoto共同工作）.利用因子分离和零维子格式消去的思想，分别给出了具有无理奇性的正规四次曲面（与Yuji石井共同工作）和指数为2的log del Pezzo曲面的分类.