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DIVISORS AND MEROMORPHIC CONVEXITY IN A STEIN SPACE

Research Project

Project/Area Number 20540180
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKumamoto University

Principal Investigator

ABE Makoto  Kumamoto University, 大学院・生命科学研究部, 准教授 (90159442)

Co-Investigator(Kenkyū-buntansha) SHIMA Tadashi  広島大学, 大学院・工学研究院, 准教授 (30226196)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords複素解析 / 複素空間 / シュタイン空間 / シュタイン多様体 / 有理型凸性 / 岡・グラウエルトの原理 / 強い円板的性質 / 有理型近似定理 / カルチエ因子 / ピカール群
Research Abstract

A Stein space is a mathematical object on which there exist sufficiently many holomorphic functions. A pseudoconvex domain in the space Cn of the n-tuples of compex numbers is a typical example of a Stein space. In this course of studies, related to the meromorphic convexity and divisors, some new results are obtained on the generalized meromorphic approximation theorem in a Stein space, on the local Steinness of a domain in a Stein orbifold satisfying the Oka-Grauert principle, and on the relation between the strong disk property and the Rungeness.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (32 results)

All 2011 2010 2009 2008 Other

All Journal Article (16 results) (of which Peer Reviewed: 6 results) Presentation (12 results) Remarks (4 results)

  • [Journal Article] Domains which satisfy the strong disk property in a Stein manifold2011

    • Author(s)
      阿部誠
    • Journal Title

      The Proceedings of the 13th Conference on Real and Complex Analysis in Hiroshima (2010)(Y.Mizuta, eds.)(Hiroshima University)

      Pages: 1-4

    • Related Report
      2010 Final Research Report
  • [Journal Article] Domains which satisfy the strong disk property in a Stein manifold2011

    • Author(s)
      Makoto Abe
    • Journal Title

      The Proceedings of the 13th Conference on Real and Complex Analysis in Hiroshima (2010), Hiroshima University, December 20-22, 2010

      Volume: 1 Pages: 1-4

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein space, Annali di Matematica Pura ed Applicata2010

    • Author(s)
      阿部誠
    • Journal Title

      Ser.4 (Online First), Published Online

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stein空間内の岡・Grauertの原理をみたす領域,函数論分科会講演アブストラクト2010

    • Author(s)
      阿部誠
    • Journal Title

      日本数学会2010年度秋季総合分科会

      Pages: 61-62

    • Related Report
      2010 Final Research Report
  • [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold, Abstract Book : 18th ICFIDCAA2010

    • Author(s)
      阿部誠
    • Journal Title

      18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, University of Macau

      Pages: 1-1

    • Related Report
      2010 Final Research Report
  • [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold2010

    • Author(s)
      Makoto Abe
    • Journal Title

      Abstract Book : 18^<th> ICFIDCAA, 18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Macau, China, August 13-17, 2010, University of Macau

      Volume: 1 Pages: 1-1

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Stein空間内の岡・Grauertの原理をみたす領域2010

    • Author(s)
      阿部誠
    • Journal Title

      函数論分科会講演アブストラクト,日本数学会2010年度秋季総合分科会,名古屋大学,20100922-20100925

      Volume: 1 Pages: 61-62

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein space2010

    • Author(s)
      Makoto Abe
    • Journal Title

      Annali di Matematica Pura ed Applicata, Ser.4 (Online First)

      Volume: 1

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Meromorphic approximation theorem with respect to a semigroup of holomorphic line bundles in a Stein space2010

    • Author(s)
      Makoto Abe
    • Journal Title

      Toyama Mathematical Journal 32(掲載確定)

    • NAID

      120002829406

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Meromorphic approximation theorem with respect to a semigroup of holomorphic line bundles in a Stein space2009

    • Author(s)
      阿部誠
    • Journal Title

      Toyama Mathematical Journal, Vol. 32

      Pages: 41-57

    • NAID

      120002829406

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] C2/Gの解析的コンパクト化について2008

    • Author(s)
      島唯史
    • Journal Title

      第51回函数論シンポジウムアブストラクト

      Pages: 47-52

    • Related Report
      2010 Final Research Report
  • [Journal Article] 成績評価における評点の算出のためのひとつの方法2008

    • Author(s)
      阿部誠
    • Journal Title

      日本数学教育学会高専・大学部会論文誌 Vol.15, no.1

      Pages: 89-96

    • NAID

      110008445236

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Meromorphic approximation in a Stein space2008

    • Author(s)
      阿部誠
    • Journal Title

      Function Spaces in Complex and Clifford Analysis (H.S. Le and W.Tutschke, eds.)(National University Publishers Hanoi)

      Pages: 100-105

    • Related Report
      2010 Final Research Report
  • [Journal Article] Meromorphic approximation in a Stein space2008

    • Author(s)
      Makoto Abe
    • Journal Title

      Function Spaces in Complex and Clifford Analysis (H. S. Le and W. Tutschke, eds. ), National University Publishers Hanoi, Hanoi

      Pages: 100-105

    • Related Report
      2008 Annual Research Report
  • [Journal Article] 成績評価における評点の算出のためのひとつの方法2008

    • Author(s)
      阿部誠
    • Journal Title

      日本数学教育学会高専・大学部会論文誌 15

      Pages: 89-96

    • NAID

      110008445236

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] C^2/Gの解析的コンパクト化について2008

    • Author(s)
      島唯史
    • Journal Title

      第51回函数論シンポジウムアブストラクト

      Pages: 47-52

    • Related Report
      2008 Annual Research Report
  • [Presentation] Domains which satisfy the strong disk property in a Stein manifold2010

    • Author(s)
      阿部誠
    • Organizer
      The 13th Conference on Real and Complex Analysis in Hiroshima
    • Place of Presentation
      広島大学,東広島市
    • Year and Date
      2010-12-20
    • Related Report
      2010 Final Research Report
  • [Presentation] Domains which satisfy the strong disk property in a Stein manifold2010

    • Author(s)
      Makoto Abe
    • Organizer
      The 13th Conference on Real and Complex Analysis in Hiroshima
    • Place of Presentation
      広島大学(東広島市)
    • Year and Date
      2010-12-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stein空間内の岡・Grauertの原理をみたす領域2010

    • Author(s)
      阿部誠
    • Organizer
      日本数学会2010年度秋季総合分科会函数論分科会
    • Place of Presentation
      名古屋大学,名古屋市
    • Year and Date
      2010-09-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Stein空間内の岡・Grauertの原理をみたす領域2010

    • Author(s)
      阿部誠
    • Organizer
      日本数学会2010年度秋季総合分科会函数論分科会
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold2010

    • Author(s)
      阿部誠
    • Organizer
      18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, University of Macau
    • Place of Presentation
      (澳門大学),中華人民共和国澳門特別行政区
    • Year and Date
      2010-08-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold2010

    • Author(s)
      Makoto Abe
    • Organizer
      18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      澳門大学(中華人民共和国澳門特別行政区)(招待講演)
    • Year and Date
      2010-08-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stein空間内のOka-Grauertの原理をみたす領域2010

    • Author(s)
      阿部誠
    • Organizer
      Hiroshima Potential Seminar
    • Place of Presentation
      広島大学,東広島市
    • Year and Date
      2010-07-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Stein空間内のOka-Grauertの原理をみたす領域2010

    • Author(s)
      阿部誠
    • Organizer
      Hiroshima Potential Seminar
    • Place of Presentation
      広島大学(東広島市)
    • Year and Date
      2010-07-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Holomorphic line bundles and Cartier divisors on domains of a Stein orbifold2008

    • Author(s)
      阿部誠
    • Organizer
      Seminario di Matematica, Scuola Normale Superiore di Pisa
    • Place of Presentation
      (ピサ高等師範学校),イタリア共和国ピサ市
    • Year and Date
      2008-10-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Holomorphic line bundles and Cartier divisors on domains of a Steinorbifold2008

    • Author(s)
      Makoto Abe
    • Organizer
      Seminario di Matematica, Scuola Normale Superiore di Pisa
    • Place of Presentation
      Scuola Normale Superioredi Pisa (イタリア共和国ピサ市)
    • Year and Date
      2008-10-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] C^2/Gの解析的コンパクト化について2008

    • Author(s)
      島唯史
    • Place of Presentation
      高知大学,高知市
    • Year and Date
      2008-10-12
    • Related Report
      2010 Final Research Report
  • [Presentation] C^2/Gの解析的コンパクト化について2008

    • Author(s)
      島唯史
    • Organizer
      第引回函数論シンポジウム
    • Place of Presentation
      高知大学(高知市)
    • Year and Date
      2008-10-12
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://se.kcn-tv.ne.jp/users/mabe/works.htm

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://se.kcn-tv.ne.jp/users/mabe/works.htm

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://se.kcn-tv.ne.jp/users/mabe/works.htm

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://se.kcn-tv.ne.jp/users/mabe/works.htm

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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