2016 Fiscal Year Final Research Report
Studies on algebraic fibered surfaces by separable quotient and purely inseparable quotient
| Project/Area Number |
25800018
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kobe University |
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Principal Investigator |
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| Research Collaborator |
NAKAMURA Iku 北海道大学, 大学院理学研究科, 名誉教授 (50022687)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 代数曲線束 / 楕円曲面 / 正標数 / 分離商 / 純非分離商 |
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| Outline of Final Research Achievements |
In algebraic geometry, the classification of algebraic varieties is one of the most fundamental problems, where algebraic varieties are classified by means of their geometric invariants. We consider the case where algebraic varieties are surfaces that are fibered over curves. We develop the methods to calculate invariants of algebraic varieties, which are important in the classification theory. Algebraic varieties are defined as the solutions of simultaneous polynomial equations. In our studies, these polynomials are defined over not only the field of complex numbers but also more general fields. In particular, in the case of fields of positive characteristic, various new phenomena appear, and we develop theories to explain them.
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| Free Research Field |
代数幾何
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