| Project/Area Number |
25400039
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
Watanabe Kenta 大阪大学, 理学(系)研究科(研究院), 研究員 (70582683)
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| Research Collaborator |
KOMEDA JIRYO 神奈川工科大学, 公私立大学の部局等, 教授 (90162065)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | K3 曲面 / 代数曲線 / Weierstrass 半群 / Lazarsfeld-Mukai 束 / ACM 束 / 非特異曲線 / クリフォード指数 / slope 安定束 / ACM ベクトル束 / 二重被覆 / ワイヤストラス半群 / 超曲面 |
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| Outline of Final Research Achievements |
In our research, we gave a concrete description and a classification of line bundles on a curve on a K3 surface which compute the Clifford index of it, by using Nikulin's concrete description of the set of fixed points of a non-symplectic involution on a K3 surface. On the other hand, we have characterized a sufficient condition for a double covering of a plane curve to be contained by a K3 surface, by using the computation of Weierstrass semigroups of ramification points on it. Moreover, later in the period, we have constructed an interesting example of an indecomposable stable vector bundle on a K3 surface in the point of view of the Brill-Noether theory of curves on regular surfaces.
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