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Value distribution theory

Research Project

Project/Area Number 18K03319
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionTokyo 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 *help
¥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.

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (9 results)

All 2022 2021 2019 2018

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (8 results) (of which Int'l Joint Research: 3 results,  Invited: 8 results)

  • [Journal Article] Holomorphic Curves and linear systems in algebraic manifolds2019

    • Author(s)
      Yoshihiro Aihara
    • Journal Title

      Analysis, Probability, Applications, and Computation , Trends in Mathematics (SpringerーBirkhauser)

      Volume: 1 Pages: 515-523

    • Related Report
      2018 Research-status Report
    • 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
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Meromorphic maps with deficiencies and the uniqueness problem2021

    • Author(s)
      相原義弘
    • Organizer
      ISAAC2021
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Holomorphic curves with deficiencies and the uniqueness problem for rmeromorphic maps2021

    • Author(s)
      相原義弘
    • Organizer
      函数論サマーセミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Deficiencies of Holomorphic curves for hypersurfaces and linear systems2019

    • Author(s)
      相原義弘
    • Organizer
      ISSAC2019  (於 アヴェイロ大学,ポルトガル)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Holomorphic curves with deficiencies2019

    • 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)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Sets of deficient divisors of a holomorphic curve in algebraic varieties2019

    • 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)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Holomorphic Curves and linear systems in projective manifolds2018

    • Author(s)
      相原義弘
    • Organizer
      値分布論研究集会(於東京大学)
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] A defect relation for holomorphic curves and linear systems in complex projective spaces2018

    • 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)
    • Related Report
      2018 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2024-01-30  

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