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2011 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 21540205
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionFukushima 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
Keywords有理型写像 / 値分布論 / 除外指数 / 一次系
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

    (20 results)

All 2012 2011 2010 2009

All Journal Article (7 results) (of which Peer Reviewed: 5 results) Presentation (13 results)

  • [Journal Article] Deficiencies of holomorphic curves in algebraic varieties2012

    • Author(s)
      相原義弘
    • Journal Title

      Tohoku Math. J

      Volume: Vol.64

    • Peer Reviewed
  • [Journal Article] Extrinsic diameter of immersed flat tori in S^3 Geometriae Dedicata2011

    • 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 diffusions2010

    • 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 Math2010

    • Author(s)
      厚地淳
    • Journal Title

      Math. Soc. Japan, Tokyo

      Volume: 57 Pages: 49-59

    • Peer Reviewed
  • [Journal Article] Submartingale properties of subharmonic functions2010

    • 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 Analysis2009

    • 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, Bull2009

    • Author(s)
      鎌田博行
    • Journal Title

      London Math. Soc

      Volume: 41 Pages: 1060-1072

    • Peer Reviewed
  • [Presentation] Another approach to Nevanlinna theory from diffusion processes2012

    • 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 curve2011

    • 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] (ア) Remarks on value distribution of leafwise meromorphic functions2011

    • 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 manifolds2011

    • 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] Extrinsic diameter of immersed flat tori in the unit 3-sphereSpanish2011

    • 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 Theory2011

    • 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] Geometric structures related to neutral metrics on complex manifolds2010

    • Author(s)
      鎌田博行
    • Organizer
      幾何学阿蘇研究会
    • Place of Presentation
      休暇村南阿蘇
    • Year and Date
      20100800
  • [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 varieties2010

    • 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] Sets of deficient divisors in linear systems2009

    • 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] Submartingale property of subharmonic functions2009

    • 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 functions2009

    • 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

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Published: 2013-07-31  

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