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2010 Fiscal Year Final Research Report

On rational functions and singularities of plane algebraic curves

Research Project

  • PDF
Project/Area Number 20540038
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionSaitama University

Principal Investigator

SAKAI Fumio  埼玉大学, 大学院・理工学研究科, 教授 (40036596)

Co-Investigator(Renkei-kenkyūsha) KOJIMA Hisashi  埼玉大学, 大学院・理工学研究科, 教授 (90146118)
FUKUI Toshizumi  埼玉大学, 大学院・理工学研究科, 教授 (90218892)
EBIHARA Madoka  埼玉大学, 大学院・理工学研究科, 講師 (80213578)
TONO Keita  埼玉大学, 大学院・理工学研究科, 非常勤講師 (30422215)
Project Period (FY) 2008 – 2010
Keywords代数幾何
Research Abstract

We studied Weierstrass points on Picard curves, 2-Weierstrass points on Kuribayashi curves and 3-Weierstrass points on genus two curves. We published papers on these topics. We also obtained new results concerning the criterion for the gonality of singular plane curves.

  • Research Products

    (14 results)

All 2011 2010 2009 2008 Other

All Journal Article (5 results) (of which Peer Reviewed: 3 results) Presentation (7 results) Book (1 results) Remarks (1 results)

  • [Journal Article] The 3-Weierstrass points on genus two curves with extra involutions2011

    • Author(s)
      Mohamed Farahat, Fumio Sakai
    • Journal Title

      Saitama Math. J

      Volume: Vol.28 Pages: 1-12

    • Peer Reviewed
  • [Journal Article] S4 geometry of Picard curves2010

    • Author(s)
      Weierstrass points, Fumio Sakai
    • Journal Title

      School in Algebraic Geometry

      Volume: Vol.3 Pages: 143-158

  • [Journal Article] Hyperelliptic plane curves of type (d, d-2)2010

    • Author(s)
      Fumio Sakai, Mohammad Saleem, Keita. Tono
    • Journal Title

      Beitrage zur Algebra und Geometri

      Volume: Vol.51 Pages: 31-44

    • Peer Reviewed
  • [Journal Article] Kamel and Geometry and computation of 2-Weierstrass points on Kuribayashi quartic curves2009

    • Author(s)
      Alwaleed, Fumio Sakai
    • Journal Title

      Saitama Math. J

      Volume: Vol.26 Pages: 67-82

    • Peer Reviewed
  • [Journal Article] Geometry of Weierstrass 3 points for 2-parameter families of plane curves2008

    • Author(s)
      Fumio Sakai
    • Journal Title

      第6回代数曲線論シンポジウム報告集

      Pages: 94-103

  • [Presentation] 平面曲線族における高次ワイエルシュトラス点の計算2011

    • Author(s)
      酒井文雄
    • Organizer
      津山代数幾何シンポジウム
    • Place of Presentation
      津山高専
    • Year and Date
      2011-07-27
  • [Presentation] On the gonality of singular plane curves II2011

    • Author(s)
      酒井文雄
    • Organizer
      アフィン代数幾何研究集会
    • Place of Presentation
      関西学院大梅田キャンパス
    • Year and Date
      2011-03-05
  • [Presentation] points Kuribayashi quartic curves2010

    • Author(s)
      酒井文雄
    • Organizer
      Tsuda College Mini-Workshop on Number Theory and Physics at the Crossroads
    • Place of Presentation
      津田塾大学
    • Year and Date
      2010-08-29
  • [Presentation] Geometry and computation of Weierstrass points2009

    • Author(s)
      酒井文雄
    • Place of Presentation
      神奈川大学富士見高原研修所
    • Year and Date
      2009-09-05
  • [Presentation] Weierstrass points and S4 geometry of Picard curves2008

    • Author(s)
      酒井文雄
    • Organizer
      A. ne Algebraic Geometry
    • Place of Presentation
      Bangalore, India
    • Year and Date
      2008-12-27
  • [Presentation] Weierstrass points and S4 geometry of Picard curves2008

    • Author(s)
      酒井文雄
    • Organizer
      Tsuda College Mini-Workshop on Number Theory and Physics at the Crossroads
    • Place of Presentation
      津田塾大学
    • Year and Date
      2008-08-05
  • [Presentation] The gonality and the genus of singular plane curves2008

    • Author(s)
      酒井文雄
    • Organizer
      2nd NIMS School in Algebraic Geometry
    • Place of Presentation
      Daejon, Korea
    • Year and Date
      2008-05-12
  • [Book] 大学数学の基礎2011

    • Author(s)
      酒井文雄
    • Total Pages
      137
    • Publisher
      共立出版
  • [Remarks]

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/FumioSakai.html

URL: 

Published: 2013-07-31  

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