Torus embedding and fiber space
| Project/Area Number |
16540025
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Kyoto University |
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Principal Investigator |
NAKAYAMA Noboru Kyoto University, Research Institute of Mathematical Sciences, Associated Professor, 数理解析研究所, 助教授 (10189079)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | toric variery / complex torus / Hodge structure / fiber space |
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| Research Abstract |
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.
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Report
(4 results)
Research Products
(8 results)
