Value distribution theory of meromorphic maps, especially on unicity problems and deficiencies on linear systems

• Project/Area Number: 21540205
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Fukushima University
• Principal Investigator: AIHARA Yoshihiro 福島大学, 人間発達文化学類, 教授 (60175718)
• Co-Investigator(Renkei-kenkyūsha): KITAGAWA Yoshihisa 宇都宮大学, 教育学部, 教授 (20144917) ; ATSUJI Astushi 慶應義塾大学, 経済学部, 教授 (00221044) ; KAMADA Hiroyuko 宮城教育大学, 教育学部, 教授 (00249799)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 有理型写像 / 値分布論 / 除外指数 / 一次系 / 正則曲線 / ネヴァンリンナ理論 / 解析的連接イデアル層 / 除外因子 / 第2主要定理 / 射影的代数多様体 / 剰余項 / Nevanlinna理論 / イデアルの連接層 / Croftonの公式

Research Abstract

We study property of Nevanlinna' s deficiency as functions on linear systems in smooth complex projective algebraic varieties. We give a structure theorem for the set of deficient divisors. This structure theorem yields that the set of values of deficiency is at most countable. Moreover, we have a correspondence between the deficiencies and the linear systems.

Research Products

• [Journal Article] Deficiencies of holomorphic curves in algebraic varieties (2012)
  • Author(s): 相原義弘
  • Journal Title: Tohoku Math. J Volume: Vol.64
  • NAID: 130005128517
  • Peer Reviewed
• [Journal Article] Deficiencies of holomorphic curves in algebraic varieties (2012)
  • Author(s): 相原義弘
  • Journal Title: Tohoku Mathematical Journal Volume: Vol.64(2)(印刷中)
  • NAID: 130005128517
  • Peer Reviewed
• [Journal Article] Extrinsic diameter of immersed flat tori in S^3 Geometriae Dedicata (2011)
  • Author(s): 北川義久and梅原
  • Volume: 155
  • Pages: 105-140
  • Peer Reviewed
• [Journal Article] On the number of omitted values by a meromorphicfunction of finite energy and heat diffusions (2010)
  • Author(s): 厚地淳
  • Journal Title: J. Geom. Anal Volume: 20no Pages: 1008-1025
  • Peer Reviewed
• [Journal Article] Estimates on the number of the omitted values bymeromorphic functions. Probabilistic approach to geometry, Adv. Stud. Pure Math (2010)
  • Author(s): 厚地淳
  • Journal Title: Math. Soc. Japan, Tokyo Volume: 57 Pages: 49-59
  • Peer Reviewed
• [Journal Article] Submartingale properties of subharmonic functions (2010)
  • Author(s): 厚地淳
  • Journal Title: 数理解析研究所講究録 Volume: 1672 Pages: 1-10
• [Journal Article] Deficiencies of holomorphic curves in algebraic manifolds, Proc. the 16th Finite or Infinite Dimensional Complex Analysis (2009)
  • Author(s): 相原義弘
  • Journal Title: eds. J. Choi et al Pages: 70-75
• [Journal Article] Indefinite K\ahler metrics of constant scalar curvatureon Hirzebruch surfaces, Bull (2009)
  • Author(s): 鎌田博行
  • Journal Title: London Math. Soc Volume: 41 Pages: 1060-1072
  • Peer Reviewed
• [Journal Article] Deficiencies of holomorphic curves in algebraic manifold (2009)
  • Author(s): 相原義弘
  • Journal Title: Proc.the 16th Int.Conference on Finite or Infinite Complex Analysys Pages: 70-75
• [Presentation] Another approach to Nevanlinna theory from diffusion processes (2012)
  • Author(s): 厚地淳
  • Organizer: International Conference in Nevanlinna Theory and Complex Geometry
  • Place of Presentation: University of Notre Dame
  • Year and Date: 2012-03-17
• [Presentation] Deficient divisors of holomorphic curve (2011)
  • Author(s): 相原義弘
  • Organizer: 第19回有限・無限次元複素解析国際会議
  • Place of Presentation: 広島
  • Year and Date: 2011-12-15
• [Presentation] Deficient divisors of holomorphic curves (2011)
  • Author(s): 相原義弘
  • Organizer: 第19回有限・無限次元複素解析とその応用国際会議
  • Place of Presentation: 広島
  • Year and Date: 2011-12-15
• [Presentation] (ア) Remarks on value distribution of leafwise meromorphic functions (2011)
  • Author(s): 厚地淳
  • Organizer: 複素解析的ベクトル場・葉層構造とその周辺
  • Place of Presentation: 龍谷大学セミナーハウスともいき荘
  • Year and Date: 2011-12-11
• [Presentation] Value distribution of meromorphic functions on foliated manifolds (2011)
  • Author(s): 厚地淳
  • Organizer: 玉原多変数複素解析研究集会
  • Place of Presentation: 東京大学玉原セミナーハウス
  • Year and Date: 2011-09-23
• [Presentation] Holomorphic curves in algebraic varieties (2011)
  • Author(s): 相原義弘
  • Organizer: 福島応用数学研究集会
  • Place of Presentation: 福島市
  • Year and Date: 2011-03-10
• [Presentation] Extrinsic diameter of immersed flat tori in the unit 3-sphereSpanish (2011)
  • Author(s): 北川義久
  • Organizer: Japanese Workshop on Differential Geometry
  • Place of Presentation: Faculty of Sicence, University of Granada
  • Year and Date: 2011-02-15
• [Presentation] Extrinsic diameter of immersed flat tori in the unit 3-sphereDifferential Geometry and Tanaka Theory (2011)
  • Author(s): 北川義久
  • Organizer: Differential System and Hypersurface Theory
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-01-25
• [Presentation] A defect relation of holomorphic curves in algebraic varieties (2010)
  • Author(s): 相原義弘
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-25
• [Presentation] Deficiencies of holomorphic curves in algebraic varieties (2010)
  • Author(s): 相原義弘
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2010-03-25
• [Presentation] S^3 内の平坦トーラスの直径に関する予想について (2010)
  • Author(s): 北川義久
  • Organizer: 名城大学幾何学研究集会
  • Place of Presentation: 名城大学(名古屋市)
  • Year and Date: 2010-03-10
• [Presentation] Deficiencies of holomorphic curves in projective varieties (2010)
  • Author(s): 相原義弘
  • Organizer: 複素解析研究集会における講演
  • Place of Presentation: 山形
  • Year and Date: 2010-01-09
• [Presentation] Deficiencies of holomorphic curves in projective varieties (2010)
  • Author(s): 相原義弘
  • Organizer: 複素解析研究集会
  • Place of Presentation: 山形・遊学館
  • Year and Date: 2010-01-09
• [Presentation] Geometric structures related to neutral metrics on complex manifolds (2010)
  • Author(s): 鎌田博行
  • Organizer: 幾何学阿蘇研究会
  • Place of Presentation: 休暇村南阿蘇
• [Presentation] Sets of deficient divisors in linear systems (2009)
  • Author(s): 相原義弘
  • Organizer: Workshop 2009 Holomorphic Mappings and Related Diophantine Approximation における講演
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2009-10-10
• [Presentation] Sets of deficient divisors in linear systems (2009)
  • Author(s): 相原義弘
  • Organizer: Tambara Workshop 2009 : Holomotphic Mappings and Related Diophantine Approximations
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2009-10-03
• [Presentation] Submartingale property of subharmonic functions (2009)
  • Author(s): 厚地淳
  • Organizer: Stochastic analysis of jump processes and related topics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-07-08
• [Presentation] ブラウン運動 (2009)
  • Author(s): 厚地淳
  • Organizer: stochastic calculusの基本事項-関数論との接点を中心に
  • Place of Presentation: 『Loewner方程式とSLE』東北大学・鳴子会館研修室
  • Year and Date: 2009-02-13
• [Presentation] Remarks on L^1-Liouville theorems and submartingale property forsubharmonic functions (2009)
  • Author(s): 厚地淳
  • Organizer: 確率論と幾何学
  • Place of Presentation: 京都大学理学部
  • Year and Date: 2009-01-10