Algebro-geometric method for singularity criteria in kinematics
| Project/Area Number |
15K13452
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hokkaido University |
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Principal Investigator |
Ohmoto Toru 北海道大学, 理学研究院, 教授 (20264400)
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| Co-Investigator(Renkei-kenkyūsha) |
Saji Kentaro 神戸大学, 大学院理学研究科, 准教授 (70451432)
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| Research Collaborator |
Kabata Yutaro 九州大学, IMI研究所, 特任助教
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 写像の特異点論 / 特異点判定法 / 射影微分幾何 / 幾何的代数 / 実代数幾何 / コンピュータ・ヴィジョン / 特性類 / 特異点判定の応用 / 局所射影微分幾何 / 射影微分幾何学 / 特異点の判定法 / アフィン代数幾何 / 同変コホモロジー |
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| Outline of Final Research Achievements |
We developed effective criteria of singularities of differentiable maps in the following three topics. 1. We have newly developed a local theory originated by Darborx and Wilcynski in projective differential geometry of surfaces in relation with applications to computer vision. 2. Combining Geometric Algebra and classification theory of map-germs, we studied singularities arising in differential line geometry (ruled surfaces, line congruences, etc), that suggests a new method in Applied Geometry. 3. Using classification of map-germs and universal polynomials of singularities, we developed classical enumerative geometry of curves and surfaces, that proposes a new algebro-geometric approach to computer vision. 4. By means of `singularity criteria', we studied A-tangent spaces and logarithmic tangents to discriminants (free divisors).
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Report
(4 results)
Research Products
(25 results)
