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Special Linear Systems on Algebraic Curves

Research Project

Project/Area Number 13640029
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokushima

Principal Investigator

OHBUCHI Akira  The University of Tokushima, 総合科学部, 教授 (10211111)

Co-Investigator(Kenkyū-buntansha) HOMMA Masaaki  The University of Tokushima, 工学部, 教授 (80145523)
KATO Takao  The University of Tokushima, 理学部, 教授 (10016157)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsAlgebraic Curve / Brill-Noether Theory / special linear system / Brill-Nother理論
Research Abstract

Let C be a smooth algebraic curve. Assume that C does not admit a double covering to another curve when C is an eve-gonal curve. We proved that if the dimension of a family of line bundles with degree d in which d is less than g-5, is more than d-3r-2, then C is a d-gonal curve with d【less than or equal】6, a 4-sheeted covering of an elliptic curve or a plane curve of degree 8. This is our first result. Next, in case 6-gonal we can prove that except a triple covering of an elliptic curve, the dimension of a family of line bundles with degree d in which d is less than g-5, should be less than d-3r-3, and in case 4-sheeted covering of an elliptic curve, the same conclusion holds.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "On the variety of special linear systems of degree g-1 on smooth algebraic curves"International Journal of Math.. 13(1). 11-29 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Homma, A.Ohbuchi: "Plane curves with aligned conductors"Far East Journal of Mathematical Sciences. 4(1). 21-53 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Kato: "Martens' dimension theorem for curves of even gonality"Korean J.Math.. 39(5). 665-680 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "Variety of nets of degree $g-1$ on smooth curves of low genus"Journal of Math.Soc.J.. 55(2)(to appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Ohbuchi, K.Konno, A.Moriwaki, N.Nakayama, S.Usui: "Proceedings of the Symposium on Algebraic Geometry in East Asia"World Scientific. 266 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K-H. Cho, C. Keem, A. Ohbuchi: "Variety of special nets of degree $g-1$ on double coverings of a smooth plane quartic of genus 9"Proc. Of ISAAC. 99. 971-986 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K-H. Cho, C. Keem, A. Ohbuchi: "On the variety of special linear systems of degree $g-1$ on smooth algebraic curves"International Journal of Math.. 13, No1. 11-29 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masaaki Hommma and Akira Ohbuchi: "Plane curves with aligned conductors"Far East J. of Math. Sci.. {\bf 4}(1). 21-53 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Kato: "Martens' dimension theorem for curves of even gonality."Korean J. Math.. {\bf 39}, 5. 665-680 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] C. Keem: "Double coverings of smooth algebraic curves"Proc. Of Algebraic Geometry in East Asia. 75-111 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K-H. Cho, C. Keem, A. Ohbuchi: "Variety of nets of degree $g-1$ on smooth curves of low genus"Journal of Math. Soc. J.. 55, No2. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A. Ohbuchi et al.: "Proceedings of the Symposium on Algebraic Geometry in East Asia"World Scientific. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "On the variety of special linear systems of degree g-1 on smooth algebraic curves"International Journal of Math.. 13(1). 11-29 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Homma, A.Ohbuchi: "Plane curves with aligned conductors"Far East Journal of Mathematical Sciences. 4(1). 21-53 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Kato: "Martens' dimension theorem for curves of even gonality"Korean J. Math.. 39(5). 665-680 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "Variety of nets of degree $g-1$ on smooth curves of low genus"Journal of Math. Soc. J.. 55(2)(to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Ohbuchi, K.Konno, A.Moriwaki, N.Nakayama, S.Usui: "Proceedings of the Symposium on Algebraic Geometry in East Asia"World Scientific. 266 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "Variety of special nets of degree g-1 on double coverings of a smooth plane quartic of genus 9"Proc. of ISAAC 99. 971-986 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Homma, A.Ohbuchi: "Plane curves with aligned conductors"Far East Journal of Mathematical Sciences. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] K-H.Cho, C.Keem, A.Ohbuchi: "On the variety of special linear system of degree g-1 on smooth algebraic curves"International Journal of Mathematics. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] E.Ballico, M.Homma, A.Ohbuchi: "On the order of speciality of a simple, special, and complete linear system on a curve"Journal of Korean Mathematical Society. (to appear).

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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