• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Applications of researches on automorhisms group of K3 surfaces to the curve theory

Research Project

Project/Area Number 25400039
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

Watanabe Kenta  大阪大学, 理学(系)研究科(研究院), 研究員 (70582683)

Research Collaborator KOMEDA JIRYO  神奈川工科大学, 公私立大学の部局等, 教授 (90162065)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsK3 曲面 / 代数曲線 / Weierstrass 半群 / Lazarsfeld-Mukai 束 / ACM 束 / 非特異曲線 / クリフォード指数 / slope 安定束 / ACM ベクトル束 / 二重被覆 / ワイヤストラス半群 / 超曲面
Outline of Final Research Achievements

In our research, we gave a concrete description and a classification of line bundles on a curve on a K3 surface which compute the Clifford index of it, by using Nikulin's concrete description of the set of fixed points of a non-symplectic involution on a K3 surface. On the other hand, we have characterized a sufficient condition for a double covering of a plane curve to be contained by a K3 surface, by using the computation of Weierstrass semigroups of ramification points on it. Moreover, later in the period, we have constructed an interesting example of an indecomposable stable vector bundle on a K3 surface in the point of view of the Brill-Noether theory of curves on regular surfaces.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (18 results)

All 2016 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Invited: 8 results) Remarks (1 results)

  • [Journal Article] On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces2016

    • Author(s)
      Kenta Watanabe
    • Journal Title

      Journal of Algebra

      Volume: 447 Pages: 445-454

    • DOI

      10.1016/j.jalgebra.2015.10.004

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On extensions of a double covering of plane curves and Weierstrass semigroups of the double covering type2015

    • Author(s)
      Jiryo Komeda, Kenta Watanabe
    • Journal Title

      Semigroup Forum

      Volume: 印刷中 Issue: 2 Pages: 517-523

    • DOI

      10.1007/s00233-015-9718-0

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The Clifford index of line bundles on a 2-elementary K3 surface given by a double cover of a Del Pezzo surface2014

    • Author(s)
      渡邉健太
    • Journal Title

      Geom. Dedicata

      Volume: 未定 Issue: 1 Pages: 347-354

    • DOI

      10.1007/s10711-014-9950-x

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Clifford index of line bundles on a 2-elementary K3 surface given by a double cover of a Del Pezzo surface2014

    • Author(s)
      Kenta Watanabe
    • Journal Title

      Geometriae Dedicata

      Volume: - Issue: 1 Pages: 329-343

    • DOI

      10.1007/s10711-014-9971-5

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] K3 曲面上の階数2 のLazarsfeld-Mukai 束のsplitting について2015

    • Author(s)
      渡邉健太
    • Organizer
      第 3 回 K3 曲面・エンリケス曲面ワークショップ
    • Place of Presentation
      北海道教育大学 札幌サテライト(教室 2)
    • Year and Date
      2015-08-17
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] K3 曲面上の階数2 のLazarsfeld-Mukai 束のsplitting について2015

    • Author(s)
      渡邉健太
    • Organizer
      ホッジ理論と代数幾何学
    • Place of Presentation
      東京電機大学(東京千住キャンパス)2号館5階2505教室
    • Year and Date
      2015-08-06
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] K3 曲面上の階数 2 の Lazarsfeld-Mukai 束の slope 安定性と ACM 直線束について2015

    • Author(s)
      渡邉健太
    • Organizer
      日本数学会 2015 年度会
    • Place of Presentation
      明治大学駿河台キャンパス リバティタワー
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 種数2 の K3 曲面上のACM 束について2014

    • Author(s)
      渡邉健太
    • Organizer
      代数多様体と その周辺
    • Place of Presentation
      琉球大学理学部
    • Year and Date
      2014-09-29 – 2014-10-02
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 種数 2 の K3 曲面上のACM 束について2014

    • Author(s)
      渡邉健太
    • Organizer
      K3 曲面・エン リケス曲面ワークショップ
    • Place of Presentation
      旭川国際会議場(旭川大雪クリスタルホール)
    • Year and Date
      2014-08-30 – 2014-09-01
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] P^3 の 4 次超曲面におけるACM 直線束の分類とその応用2014

    • Author(s)
      渡邉健太
    • Organizer
      日大(月曜)特異点セミナー
    • Place of Presentation
      日本大学文理学部 8 号館
    • Year and Date
      2014-06-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] タイトル:P^3 の 4 次超曲面における ACM 直線束の分類とその応用について2014

    • Author(s)
      渡邉健太
    • Organizer
      第 6 回代数曲面ワークショップ at 秋葉原
    • Place of Presentation
      首都大学東京秋葉原サテライトキャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] P^3 の 4 次超曲面における ACM 直線束の分類について2014

    • Author(s)
      渡邉健太
    • Organizer
      日本数学会 2014 年度会
    • Place of Presentation
      学習院大学理学部数学教室
    • Related Report
      2013 Research-status Report
  • [Presentation] On the classification of ACM line bundles on quartic hypersurfaces of P^32013

    • Author(s)
      渡邉健太
    • Organizer
      第 11 回代数曲線論シンポジウム
    • Place of Presentation
      首都大学東京南大沢キャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] DelPezzo 曲面の二重被覆として得られる(ある種の) K3 曲面上の直線束のクリフォード指数2013

    • Author(s)
      渡邉健太
    • Organizer
      代数幾何学セミナー
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On the classification of ACM line bundles on quartic hypersurfaces on P^32013

    • Author(s)
      渡邉健太
    • Organizer
      代数幾何学城崎シンポジウム 2013(ポスター発表)
    • Place of Presentation
      兵庫県立城崎大会議館
    • Related Report
      2013 Research-status Report
  • [Presentation] 平面曲線の二重被覆の拡張と二重被覆型のワイヤストラス半群について2013

    • Author(s)
      渡邉健太
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学理学部
    • Related Report
      2013 Research-status Report
  • [Presentation] P^3 の4次超曲面における算術的コーエン・マコーレー直線束の特徴づけについて2013

    • Author(s)
      渡邉健太
    • Organizer
      K3 曲面・エンリケス曲面ワークショップ
    • Place of Presentation
      北海道教育大学札幌駅前サテライト教室3
    • Related Report
      2013 Research-status Report
  • [Remarks] 渡邉健太のページ

    • URL

      http://www.geocities.jp/kenta314_math/

    • Related Report
      2015 Annual Research Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi