2003 Fiscal Year Final Research Report Summary
Etale endomorphisms of algebraic varieties
| Project/Area Number |
13440009
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kwansei Gakuin University (2003)
Osaka University (2001-2002) |
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Principal Investigator |
MIYANISHI Masayoshi Kwansei Gakuin University, School of Science & Technology, Professor, 理工学部, 教授 (80025311)
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| Co-Investigator(Kenkyū-buntansha) |
USUI Sanpei Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90117002)
HIBI Takayuki Osaka University, Graduate School of Science, Professor, 大学院・情報科学研究科, 教授 (80181113)
FUJIKI Akira Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80027383)
SHINOHARA Yaichi Kwansei Gakuin University, School of Science & Technology, Associate Professor, 理工学部, 教授 (10098303)
MASUDA Kayo University of Hyougo, Graduate School of Material Science, Professor, 大学院・物質理学研究科, 助教授 (40280416)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Etale endomorphism / Q-homology planes / Algebraic surfacees with group actions / Twister spaces / Groebner basis / Computational algebras / Toroidal compactification / pretzel link |
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| Research Abstract |
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.
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