2016 Fiscal Year Final Research Report
Geometric properties of Veech groups
| Project/Area Number |
15H06251
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Research Collaborator |
Iguchi Yuki 東京工業高等専門学校, 一般教育科, 助教 (10756795)
Amano Masanori 静岡県立大学, 経営情報学部経営情報学科, 助教 (60793867)
Yamaki Daisuke 東京工業大学, 理工学研究科, 教務補佐委員
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Keywords | Veech群 / Veech曲面 / タイヒミュラー空間 / タイヒミュラー曲線 / リーマン面 |
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| Outline of Final Research Achievements |
In the first year, I aim to give an inequality to compare the signatures of Veech groups with ratios of moduli for arithmetic Veech surfaces. I gave an comparison between the signatures of Veech groups and degrees of Veech surfaces as branched coverings of tori. However, this comparison needs to be improved.
In the last year, I study properties of trees on Teichmuller disks. It is known that every point of the trees are corresponding to Veech surfaces. I found that each edge of such tree have a point corresponding to a Veech surface with certain good property. I also gave a geometrical meaning of such points.
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| Free Research Field |
函数論
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