DIVISORS AND MEROMORPHIC CONVEXITY IN A STEIN SPACE

• Project/Area Number: 20540180
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kumamoto 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: ¥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.

Research Products

• [Journal Article] Domains which satisfy the strong disk property in a Stein manifold (2011)
  • 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
• [Journal Article] Domains which satisfy the strong disk property in a Stein manifold (2011)
  • 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
• [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein space, Annali di Matematica Pura ed Applicata (2010)
  • Author(s): 阿部誠
  • Journal Title: Ser.4 (Online First), Published Online
  • 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
• [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold, Abstract Book : 18th ICFIDCAA (2010)
  • 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
• [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold (2010)
  • 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
• [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
• [Journal Article] Open sets which satisfy the Oka-Grauert principle in a Stein space (2010)
  • Author(s): Makoto Abe
  • Journal Title: Annali di Matematica Pura ed Applicata, Ser.4 (Online First) Volume: 1
  • Peer Reviewed
• [Journal Article] Meromorphic approximation theorem with respect to a semigroup of holomorphic line bundles in a Stein space (2010)
  • Author(s): Makoto Abe
  • Journal Title: Toyama Mathematical Journal 32(掲載確定)
  • NAID: 120002829406
  • Peer Reviewed
• [Journal Article] Meromorphic approximation theorem with respect to a semigroup of holomorphic line bundles in a Stein space (2009)
  • Author(s): 阿部誠
  • Journal Title: Toyama Mathematical Journal, Vol. 32 Pages: 41-57
  • NAID: 120002829406
  • 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
• [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
  • Peer Reviewed
• [Journal Article] Meromorphic approximation in a Stein space (2008)
  • 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
• [Journal Article] Meromorphic approximation in a Stein space (2008)
  • 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
• [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
  • 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
• [Presentation] Domains which satisfy the strong disk property in a Stein manifold (2010)
  • 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
• [Presentation] Domains which satisfy the strong disk property in a Stein manifold (2010)
  • 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
• [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
• [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
• [Presentation] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold (2010)
  • 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
• [Presentation] Open sets which satisfy the Oka-Grauert principle in a Stein orbifold (2010)
  • 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
• [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
• [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
• [Presentation] Holomorphic line bundles and Cartier divisors on domains of a Stein orbifold (2008)
  • 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
• [Presentation] Holomorphic line bundles and Cartier divisors on domains of a Steinorbifold (2008)
  • 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
• [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
• [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
• [Remarks] ホームページ等
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