Geometry of Degenerations of Riemann Surfaces

• Project/Area Number: 20540073
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: TAKAMURA Shigeru 京都大学, 大学院・理学研究科, 准教授 (20362436)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: リーマン面 / 分裂変形 / 複素曲面 / 特異点 / モノドロミー / リーマン面の退化 / デーン・ツイスト / 複素幾何 / モジュライ空間 / 退化族 / 複素構造 / デーン・シイスト / テータ関数

Research Abstract

We studied degenerations of Riemann surfaces from the viewpoint of low-dimensional topology, algebraic geometry and singular theory. We described holomorphic maps on resolution spaces and described circle actions around the critical sets. We applied these descriptions to those of topological monodromies. Moreover, we generalized a part of these results to the higher-dimensional case. We proved that the quotient of A-singularity under a cyclic group action is uniformized by a small group.

Research Products

• [Journal Article] Splittability of stellar singular fibers with three branches (2006)
  • Author(s): K. Ahara, and S. Takamura
  • Journal Title: Tokyo J. Math Volume: 29 Pages: 17-17
• [Journal Article] Splittability of stellar singular fibers with three branches (2006)
  • Author(s): K.Ahara, S.Takamura
  • Journal Title: Tokyo J.Math. 29 Pages: 1-17
• [Journal Article] Towards the Classification of Atoms of Degenerations, I(Splitting Criteria via Configurations of Singular Fibers) (2004)
  • Author(s): S. Takamura
  • Journal Title: J. Math. Soc. Japan Volume: 56(1) Pages: 115-145
  • NAID: 10013122628
• [Journal Article] Towards the Classification of Atoms of Degenerations, I (Splitting Criteria via Configurations of Singular Fibers) (2004)
  • Author(s): S.Takamura
  • Journal Title: J.Math.Soc.Japan 56(1) Pages: 115-145
  • NAID: 10013122628
• [Presentation] Singularities, monodromies and uniformization (2012)
  • Author(s): 高村茂、佐々木建祀郎
  • Organizer: 研究集会「接触構造・特異点・微分方程式およびその周辺」
  • Place of Presentation: 鹿児島大学理学部大会議室(招待講演)
  • Year and Date: 2012-01-19
• [Presentation] 接触構造・特異点・微分方程式およびその周辺 (2012)
  • Author(s): 高村茂、佐々木建祀郎
  • Organizer: 鹿児島大学理学部大会議室
• [Presentation] Singular fibers of degenerafions of Riemann sarfaces (2009)
  • Author(s): 高村茂
  • Organizer: Branched coverings, Degenerations, and Related Topics
  • Place of Presentation: 広島大学
  • Year and Date: 2009-03-12
• [Presentation] Branched Coverings, Degenerations, and Related Topics (2009)
  • Author(s): 高村茂
  • Organizer: 広島大学数学教室
• [Presentation] 「Singular fibers of degenerations of Riemann surfaces」3月12日 (2009)
  • Author(s): 松本幸夫, 足利正, 作間誠, 徳永浩雄, 島田伊知朗
  • Organizer: Branched Coverings, Degenerations, and Related Topics
  • Place of Presentation: 広島大学数学教室
• [Presentation] 分裂族、モノドロミー、チャート箱根セミナー06 (2006)
  • Author(s): 高村茂
  • Organizer: 日小田急箱根レイクホテル
  • Year and Date: 2006-01-29
• [Presentation] Canonical projection of degenerations (2006)
  • Author(s): 松本幸夫
  • Organizer: 分裂族、モノドロミー、チャート 箱根セミナー06
  • Place of Presentation: 小田急箱根レイクホテル
  • Year and Date: 2006-01-29
• [Book] Towards the classification of atoms of degenerations, III(Splitting Deformations of Degenerations of Complex Curves) (2006)
  • Author(s): S. Takamura
  • Total Pages: 590
  • Publisher: Springer Lecture Notes in Math
• [Book] Springer Lecture Notes in Math.1886(Towards the classification of atoms of degenerations, III (Splitting Deformations of Degenerations of Complex Curves)) (2006)
  • Author(s): S.Takamura
  • Total Pages: 590
• [Remarks] ホームページ
  • URL: http://www.math.kyoto-u.ac.jp/~takamura/
• [Remarks]