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Splittings of degenerafions of Riemann surfaces

Research Project

Project/Area Number 16540062
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

TAKAMURA Shigeru  Kyoto University, Graduate School of Science, Associate Professor (20362436)

Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,870,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
KeywordsRiemann surface / splitting / simgularity / monodromy / complex stracture / complex surface / moduli / theta function / モジュライ空間 / 複素構造の変形 / データ関数
Research Abstract

Consider a family fo Riemann surfaces with a slaguar fiber (a degeneration), Its topological type is determined by its topological monodromy (Matsumoto-Montesinos Theorem). If the topological monodromy is periodic, then the sluguar fiber is star-shaped ite core with branches, For a particular cure where the core is a Riemann sphere and the number of branches is exactly three, my joint work with Kazushi Ahara (Meiji Univ). Showed that such a degeneration necessarily hao a splitting deformation. The proof is based on my splittability criterion is terms of the existence of a shbdivisor (called a crust) of the singular fiber, The latter work is published an Springer Lecture Notes in Math 1886. We however remark that if the number of braches if at least four, then these is some cate where my criterion does not work, but it' may possibly have a splitting family. this is also a challenging problem to consider.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (8 results)

All 2006

All Journal Article (4 results) (of which Peer Reviewed: 1 results) Presentation (2 results) Book (2 results)

  • [Journal Article] Splittability of stellar sungular Fiber with Three branches2006

    • Author(s)
      Kazushi Ahara, Shigeru Takamura
    • Journal Title

      Tokyo Journal of Mathematics 29

      Pages: 1-17

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Splittability of Stellar Singular Fiber with Three branches2006

    • Author(s)
      Kazushi, Ahara, Shigeru, Takamura
    • Journal Title

      Tokyo Journal of Math 29

      Pages: 1-17

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Splitting deformations of degenenerations of complex curves2006

    • Author(s)
      Shigera, Takamura
    • Journal Title

      Springer

      Pages: 590-590

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Splittability of Stellar Singular Fiber with Three branches2006

    • Author(s)
      Kazushi Ahara, Shigeru Takamura
    • Journal Title

      Tokyo Journal of Mathematics 29・1

      Pages: 1-17

    • Related Report
      2006 Annual Research Report
  • [Presentation] Canonical Projections of Degenerations2006

    • Author(s)
      Shigeru Takamura
    • Organizer
      分裂, モノドロミー, チャート
    • Place of Presentation
      箱根
    • Year and Date
      2006-01-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Canonial Projections of Pegenerations2006

    • Author(s)
      Shigera, Takamura
    • Organizer
      Splitting, monodromy, chart
    • Place of Presentation
      Hakone
    • Year and Date
      2006-01-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Splitting deformations of degenerations of complex curves2006

    • Author(s)
      Shigeru Takamura
    • Total Pages
      590
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Splitling deformations of degenerations of complex carves2006

    • Author(s)
      Shigeru Takamura
    • Total Pages
      590
    • Publisher
      Springer
    • Related Report
      2006 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

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