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Etale endomorphisms of algebraic varieties

代数簇的 Etale 自同态

基本信息

批准号：
13440009
负责人：
MIYANISHI Masayoshi
金额：
$ 6.53万
依托单位：
Kwansei Gakuin University (2003)Osaka University (2001-2002)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440009/
关键词：
Etale endomorphism Q-homology planes Algebraic surfacees with group actions Twister spaces Groebner basis Computational algebras Toroidal compactification pretzel link 普遍被覆アフィン擬平面 BMO関数 link Jones多項式加法群スキームシンプレクティック多様体 Moi

项目摘要

1.Head investingator, in collaboration with K.Masuda, considered etale endomorphisms of algebraic surfacees admitting G_m-actions and showed that they are automorphisms almost in all cases. On the other hand, he considered a classification of algebraic surfacees with finite group actions arid showed that we can make parallel arguments with the case without group actions but need more subtle arguments. Furthermore, he with K. Masuda considered Q-homology planes admitting two algebraically independent G_a-actions and showed that their universal coverings are hypersurfaces defined by xy=z^2-1.2.A.Fujiki considered self-dual metrics for a(differentiable) connected sum mP^2 of the projective plane and associated twister spaces(3-dimensional complex manifolds) and observed maximal value of algebraic dimension which twister spaces can take for various metrics. He obtained many results on the related topics.3.T.Hibi considered the Groebner basis of the toric ideal associated with the normalized volumes of configurations related with root systems and complete bipartite graphs. He obtained many results on computational algebras.4.S.Usui, in collaboration with K.Kato, realized a so-called Griffith's dream by considering the toroidal compactification of a symmetric space Γ＼D, when D has polarized Hodge structures.5.Y.Shinohara considered the generalized pretzel links and computed the associated Jones polynomials.

1.与K.增田合作，研究了容许G_m作用的代数曲面的自同态，并证明了它们几乎在所有情况下都是自同构.另一方面，他认为一个分类的代数surfacees有限组行动和表明，我们可以平行的论点的情况下，没有组行动，但需要更微妙的论点。他与K。增田考虑了允许两个代数独立的G_a-作用的Q-同调平面，并证明了它们的泛覆盖是由xy=z^2- 1.2定义的超曲面。藤木考虑了射影平面和相关的twister空间（三维复流形）的（可微）连通和mP^2的自对偶度量，并观察到twister空间在各种度量下所能取的代数维数的最大值。他获得了许多结果的相关主题。3.T.Hibi认为Groebner基础的环面理想与正规化卷的配置有关的根系和完全二分图。他在计算代数方面获得了许多结果。4.S.Shohari与K.Kato合作，通过考虑对称空间Γ\D的环面紧化实现了所谓的Griffith梦想，当D具有极化Hodge结构时。