A study on dynamical system for a torus and cohomology

环面动力系统与上同调的研究

• 批准号: 12640183
• 负责人: KAZAMA Hideaki
• 金额: $ 2.11万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640183/
• 关键词: line bundle; Kodaira's lemma; toroidal group; 複素トーラス; 力学系; 解析的コモホロジー群; 擬アーベル多様体; 線形化可能性; 連分数展開; 解析的コホモロジー群; コホモロジーの非ハウスドルフ性; 擬凸性

(I) It is a problem whether one can embed a weakly 1-complete manifold with a positive line bundles into a projective space by sections of higher tensor power positive line bundles, or not. It is a very interesting result that one can embed a weakly 1-complete manifold with a positive line bundle by sections of adjoint line bundles instead of the original line bundle by Shigeharu Takayama. This result is proved by a similar method in case of compact manifolds. We apply this method by adjoint line bundle to a problem of line bundle convexity. We get some global result with respect to line bundle convexity of weakly 1-complete manifolds.(ii) Recently we find an example that Kodaira's lemma does not hold for some strongly 1-complete manifold. Now we try to characterize strongly 1-complete manifolds on which Kodaira's lemma holds alway.(iii) On troidal groups of cohomologically finite type we can apply the theory of compact Kaehler manifolds. For instance we can show the Hodge decomposition theorem for toroidal groups of cohomologically finite type. We are getting some result for them similar to the results of compact Kaehler manifolds.

（i）是否可以通过较高的张量电源正线束的部分嵌入一个弱的1个完整的歧管，将正线束嵌入投影空间。一个非常有趣的结果是，一个人可以通过隔行线束的部分而不是Shigeharu takayama的原始线条捆绑包嵌入一个弱的1个完全歧管。在紧凑型歧管的情况下，通过类似的方法证明了这一结果。我们将此方法列于伴随线捆绑包到线束凸度的问题。我们在弱1完全歧管的线束凸音方面获得了一些全局结果。（ii）最近，我们发现一个例子，即Kodaira的引理无法满足某些强烈的1份歧管。现在，我们尝试表征Kodaira的引理一直保持着强烈的1个完整歧管。例如，我们可以向共同体有限类型的旋风组显示Hodge分解定理。我们正在为它们获得一些结果，类似于紧凑的Kaehler歧管的结果。

项目成果

Jyouichi Kaneko: "Classification of Pfaffian systems of Fuchs type of a particular class"Kumamoto J. Math. 15. 17-52 (2002)

Jyouichi Kaneko：“特定类别的 Fuchs 类型的普法夫系统的分类”Kumamoto J. Math。

Kazama,H.,Kim,D.K.and C.Y.Oh: "Some remarks on complex Lie groups"Nagoya Math.J.. 157. 47-57 (2000)

Kazama,H.,Kim,D.K.和C.Y.Oh：“关于复杂李群的一些评论”Nagoya Math.J.. 157. 47-57 (2000)

Koji Cho: "Characterizations of projective space and applications to complex symplectic manifolds"Adv. Stud. Pure Math.. 35. 1-88 (2002)

Koji Cho：“射影空间的表征及其在复辛流形中的应用”Adv。

Kazama,H.and Takayama,S.: "On the dd'-equation over pseudoconvex Kaehler manifolds"Manuscripta Math., Springer Verlag. 102. 25-39 (2000)

Kazama, H. 和 Takayama, S.：“关于伪凸凯勒流形上的 dd 方程”Manuscripta Math.，Springer Verlag。

Hideaki Kazama: "Nonlinearizability non-Hausdorff cohomology and neighborhood structure of elliptic curves"Complex Analysis and Related Topics in Mathematics, 2001. 67-74 (2002)

风间英明：《椭圆曲线的非线性化非豪斯多夫上同调和邻域结构》数学复数分析及相关专题，2001. 67-74 (2002)