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Geometric properties of Veech groups

Research Project

Project/Area Number 15H06251
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionShizuoka University

Principal Investigator

Shinomiya Yoshihiko  静岡大学, 教育学部, 講師 (40755930)

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
Project Period (FY) 2015-08-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
KeywordsVeech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 / Teichmuller空間 / Teichmuller曲線 / Riemann面
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.

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • Research Products

    (2 results)

All 2017 2016

All Presentation (2 results)

  • [Presentation] Veech 曲面の幾何2017

    • Author(s)
      四之宮佳彦
    • Organizer
      2次微分の幾何とその周辺
    • Place of Presentation
      東京大学大学院数理科学研究科 (東京都目黒区駒場)
    • Year and Date
      2017-01-11
    • Related Report
      2016 Annual Research Report
  • [Presentation] Veech 曲面の幾何2016

    • Author(s)
      四之宮佳彦
    • Organizer
      第59回函数論シンポジウム
    • Place of Presentation
      静岡県男女共同参画センター あざれあ (静岡県静岡市葵区)
    • Year and Date
      2016-10-08
    • Related Report
      2016 Annual Research Report

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Published: 2015-08-26   Modified: 2018-03-22  

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