Value distribution theory

• Project/Area Number: 18K03319
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Tokyo Gakugei University (2022); Fukushima University (2018-2021)
• Principal Investigator: AIHARA Yoshihiro 東京学芸大学, 教育学部, 研究員 (60175718)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 正則曲線 / 有理型写像 / 値分布論 / 除外指数 / 除外因子 / 一次系 / 一意性問題 / 一意性定理 / 除外値 / ネヴァンリンナ理論 / Nevanlinna理論 / 退化定理

Outline of Final Research Achievements

The investigator study the structure of deficient divisor of holomorphic curves in algebraic varieties. He give an structure theorem on the set of deficient divisors. Hw also show that there are holomorophic curves with deficiencies.

Academic Significance and Societal Importance of the Research Achievements

本研究は多変数複素解析において，複素多様体間の有理型写像の定量的研究に関するものである．特に超越性が引き起こす写像に対する様々な性質の解明に資するものである．本研究は複素解析学・複素解析幾何学において基本的な重要性を持つ．多変数複素解析学は現在では物理学・情報分野の様々な分野で応用がなされており，写像の性質の解明することは多方面への応用も期待される．

Research Products

• [Journal Article] Holomorphic Curves and linear systems in algebraic manifolds (2019)
  • Author(s): Yoshihiro Aihara
  • Journal Title: Analysis, Probability, Applications, and Computation , Trends in Mathematics (SpringerーBirkhauser) Volume: 1 Pages: 515-523
  • Peer Reviewed
• [Presentation] 代数多様体内の正則曲線の値分布，特に高次元Nevanlinna理論とその周辺 (2022)
  • Author(s): 相原義弘
  • Organizer: Seminar on complex analytic geometry in Shizuoka
  • Invited
• [Presentation] Meromorphic maps with deficiencies and the uniqueness problem (2021)
  • Author(s): 相原義弘
  • Organizer: ISAAC2021
  • Int'l Joint Research / Invited
• [Presentation] Holomorphic curves with deficiencies and the uniqueness problem for rmeromorphic maps (2021)
  • Author(s): 相原義弘
  • Organizer: 函数論サマーセミナー
  • Invited
• [Presentation] Deficiencies of Holomorphic curves for hypersurfaces and linear systems (2019)
  • Author(s): 相原義弘
  • Organizer: ISSAC2019 (於 アヴェイロ大学，ポルトガル）
  • Int'l Joint Research / Invited
• [Presentation] Holomorphic curves with deficiencies (2019)
  • Author(s): 相原義弘
  • Organizer: 有限無限次元複素解析国際会議（於 シベリア中央大学，ロシア）
  • Int'l Joint Research / Invited
• [Presentation] Sets of deficient divisors of a holomorphic curve in algebraic varieties (2019)
  • Author(s): 相原義弘
  • Organizer: 等角写像論・値分布論合同研究集会 （於 東北大学）
  • Invited
• [Presentation] Holomorphic Curves and linear systems in projective manifolds (2018)
  • Author(s): 相原義弘
  • Organizer: 値分布論研究集会（於東京大学）
  • Invited
• [Presentation] A defect relation for holomorphic curves and linear systems in complex projective spaces (2018)
  • Author(s): 相原義弘
  • Organizer: 等角写像論・価分布論合同研究集会 (於大阪府立大学）
  • Invited