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2006 Fiscal Year Final Research Report Summary

Algebraic Curves and its Applications

Research Project

Project/Area Number 17540030
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, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (10211111)

Co-Investigator(Kenkyū-buntansha) KATO Takao  YamaguchiUniversity, Faculty of Science, Professor, 理学部, 教授 (10016157)
KOMEDA Jiryo  Kanagawa Institute of Technology, Department of Mathematics, Professor, 工学部, 教授 (90162065)
KONNO Kazuhiro  Osaka University, Faculty of Science, Professor, 大学院・理学研究科, 教授 (10186869)
NAMBA Makoto  Ohtemon University, College of Economics, Professor, 経済学部, 教授 (60004462)
HOMMA Masaaki  Kanagawa University, Department of Mathematics, Professor, 工学部, 教授 (80145523)
Project Period (FY) 2005 – 2006
KeywordsAlgebraic Curve / Special Linear System / Brill-Nother Theory
Research Abstract

Let W^r_d (C)
be a scheme of line bundles defined by usually, can be defined as a subscheme of Pic^d (C)). Kempfand Kleiman-Laksov prove that the variety W^r_d (C) hasdimension at least p = g-(r+1)(g-d+r). Griffith -Harris and Fulton-Lazarsfeld prove that W^r_d(C) is smooth of dimension p = g-(r+1)(g-d+r) when C is a general curve in the moduli space M_g. "A general curve" means there is an open subset U⊂M_g in M_g, W^r_d(C) is smooth of dimension p = g-(r+1)(g-d+r) for any curve C ∈ U. For a curve C which admits a double covering π:C→E to a curve E of genus h, i.e. a curve which we can not regard as a general curve, we can expect many interesting structure of W^r_d (C). In the papers, we give many good properties of W^r_d(C), especially W^1_d(C).

  • Research Products

    (4 results)

All 2007 Other

All Journal Article (4 results)

  • [Journal Article] On the Castelnuovo-Severi inequality for a double covering2007

    • Author(s)
      Ohbuchi, Akira
    • Journal Title

      Proceedings of Algebraic Geometry in East Asia II (Hanoi)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the Castelnuovo-Severi inequality for a double covering

    • Author(s)
      C.Keem, A.Ohbuchi
    • Journal Title

      Proceedings of Algebraic Geometry in East Asia II (Hanoi) (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On double coverings of a pointed non-singular curve with any VVeier strass semigroup

    • Author(s)
      J.Komeda, A.Ohbuchi
    • Journal Title

      Tsukuba J. Math. (印刷中)(To appear)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On double coverings of a pointed non-singular curve with any Weierstrass semigroup

    • Journal Title

      Tsukuba J. Math. (To appear)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2008-05-27  

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