Studies on local invariants of degeneration of algebraic curves via moduli map and monodromy

• Project/Area Number: 19540047
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku Gakuin University
• Principal Investigator: ASHIKAGA Tadashi Tohoku Gakuin University, 工学部, 教授 (90125203)
• Co-Investigator(Kenkyū-buntansha): KONNO Kazuhiro 大阪大学大学院, 理学研究科, 教授 (10186869) ; ISHIDA Hirotaka 宇部工業高等専門学校, 一般科, 講師 (30435458)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2007: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 代数曲面 / 退化 / 曲線族 / 符号数 / 局所化 / モノドロミー / モジュライ空間 / リーマン面 / 特異点 / Horikawa指数 / ファイバー空間 / 複素曲面 / 代数曲線 / モジュライ

Research Abstract

退化代数曲線族の局所符号数を、安定曲線のモジュライ空間上の符号数因子とエータ不変量の群作用に関する変動項をモノドロミー情報に還元することを用いて、明示的に表示する道を開くことができた。また関連する代数曲面上のペンシルや特異点についても、有用な進展があった。

Research Products

• [Journal Article] On the fixed loci of the canonical systems over normal surface singularities (2008)
  • Author(s): Kazuhiro Konno
  • Journal Title: Asian J. of Math 12, no.4 Pages: 449-464
• [Journal Article] On the cohomological cycle of a normal surface singularity (2008)
  • Author(s): Kazuhiro Konno
  • Journal Title: RIMS Kokyuroku Bessatsu B9 Pages: 143-151
• [Journal Article] The base components of the dualizing sheaf of a curve on a surface (2008)
  • Author(s): Kazuhiro Konno and Margarida Mendes Lopes
  • Journal Title: Archiv der Mathematik90 no.5 Pages: 395-400
• [Journal Article] Minimal pencils on smooth surfaces in P^3 (2008)
  • Author(s): Kazuhiro Konno
  • Journal Title: Osaka Math. J. 45 no.3 Pages: 789-805
• [Journal Article] Relations in the canonical algebras on surfaces (2008)
  • Author(s): Kazuhiro Konno
  • Journal Title: Rend. Sem. Mat. Univ. Padova 120 Pages: 227-261
• [Journal Article] On certain fibred rational surfaces (2008)
  • Author(s): Kazuhiro Konno
  • Journal Title: Kodai Math J.31 no.1 Pages: 21-37
  • NAID: 130004687878
• [Journal Article] On certain fibered rational surfaces (2008)
  • Author(s): K. Konno
  • Journal Title: Kodai Math.J. 31 Pages: 21-37
  • Peer Reviewed
• [Journal Article] The base componentsof the dualizing sheaf of a curve on a surface (2008)
  • Author(s): K. Konno and M. Mendes Lopes
  • Journal Title: Archiv der Mathematik 90 Pages: 395-400
  • Peer Reviewed
• [Journal Article] A divisor on the moduli space of curves associated to the signature of fibered surfaces, to appear in Adv
  • Author(s): Tadashi Ashikaga and Ken-ichi Yoshikawa
  • Journal Title: Studies in Pure Math
• [Journal Article] Another form of the reciprocity law of Dedekind sum
  • Author(s): Tadashi Ashikaga and Mizuho Ishizaka
  • Journal Title: to appear in Revista Math
• [Journal Article] Appendix to "A divisor on the moduli space of curves associated to the signature of fibered surfaces"
  • Author(s): Kazuhiro Konno
  • Journal Title: preprint(2008)to appear in Proceedings of Singularities, Niigata -Toyama
• [Journal Article] Triple covers of algebraic surfaces and a generalization of Zariski's Example, to appear in Adv
  • Author(s): Hirotaka Ishida and Hiro-o tokunaga
  • Journal Title: Studies in Pure Math
• [Journal Article] A divisor on the moduli space of curves associated with the signature of fibered surfaces
  • Author(s): T. Ashikaga, K. Yoshikawa
  • Journal Title: Advanced studies in Pure Math. (掲載予定)
  • Peer Reviewed
• [Journal Article] Another form of the reciprocity law of Dedekind sum
  • Author(s): T. Ashikaga, M. Ishizaka
  • Journal Title: Revista Math. (掲載予定)
  • Peer Reviewed
• [Journal Article] Local signature defect of fibered complex surfaces via monodromy and stable reduction
  • Author(s): T. Ashikaga
  • Journal Title: (現在投稿中)
  • Peer Reviewed
• [Presentation] signature divisor on the moduli space of curves and its application (2009)
  • Author(s): 足利 正
  • Organizer: 第4回代数・幾何・解析セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2009-02-17
• [Presentation] Eta invariant and local signature of degeneration of Riemann surfaces, Symposium on Branched coverings (2009)
  • Author(s): 足利正
  • Organizer: Degenerations and Related topics
  • Place of Presentation: 広島大学
• [Presentation] 曲線の退化ファイバー芽のエータ不変量に関する一考察 (2009)
  • Author(s): 足利正
  • Organizer: 代数幾何学ミニワークショップ
  • Place of Presentation: 兵庫県八千代町
• [Presentation] Signature divisor on the moduli space of curves and its application (2009)
  • Author(s): 足利正
  • Organizer: 第4回代数・幾何・解析セミナー
  • Place of Presentation: 鹿児島大学
• [Presentation] 2次元数値的Gorenstein特異点に対するNoether型不等式 (2009)
  • Author(s): 今野一宏
  • Organizer: 代数幾何学in九州
  • Place of Presentation: 九州大学箱崎キャンパス
• [Presentation] 標準サイクルの鎖分解と特異ファイバー (2008)
  • Author(s): 今野 一宏
  • Organizer: Hodge理論・退化・特異点の代数幾何とトポロジー(第4回)
  • Place of Presentation: 東北学院大学
  • Year and Date: 2008-03-14
• [Presentation] A new formula for Dedekind sum and the signature of fibered surfaces (2008)
  • Author(s): 足利 正・石坂 瑞穂
  • Organizer: Hodge理論・退化・特異点の代数幾何とトポロジー(第4回)
  • Place of Presentation: 東北学院大学
  • Year and Date: 2008-03-12
• [Presentation] ある特異曲線の存在性について (2008)
  • Author(s): 石田 弘隆
  • Organizer: 研究集会「被覆のつどい」(第2回)
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-01-13
• [Presentation] Remarks on the Castelnuovo-Horikawa index (2008)
  • Author(s): 足利 正
  • Organizer: 研究集会「被覆のつどい」(第2回)
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-01-12
• [Presentation] Localization of the signature of fibered complex surfaces (2008)
  • Author(s): T.Ashikaga
  • Organizer: International Conference on finite and infinite dimensional complex analysis and its application, Gyengju Univ. KOREA
• [Presentation] Dedekind和の相互律の幾何と新公式 (2008)
  • Author(s): 足利正, 石坂瑞穂
  • Organizer: Hodge理論・退化・特異点の代数幾何とトポロジー研究集会(第4回)
  • Place of Presentation: 東北学院大学
• [Presentation] Remarks on Horikawa index (2008)
  • Author(s): 足利正
  • Organizer: 分岐被覆に関連する代数幾何ミニワークショップ
  • Place of Presentation: 兵庫県八千代町
• [Presentation] Invariants of fiber germs and surface singularities (2008)
  • Author(s): 足利正
  • Organizer: 分岐被覆に関連する代数幾何とトポロジー(第2回)
  • Place of Presentation: 首都大学東京
• [Presentation] Chain-decompositions of canonical cycles (2008)
  • Author(s): K.Konno
  • Organizer: Geometry of Singularities and Manifolds
  • Place of Presentation: 草津セミナーハウス
• [Presentation] 標準サイクルの鎖分解と特異ファイバー, Hodge理論, 退化 (2008)
  • Author(s): 今野一宏
  • Organizer: 特異点の代数幾何とトポロジー
  • Place of Presentation: 東北学院大学工学部
• [Presentation] 被覆による特異曲線の構成 (2008)
  • Author(s): 石田弘隆
  • Organizer: 津山代数幾何シンポジューム
  • Place of Presentation: 津山工業高等専門学校
• [Presentation] Constructions of certain singular curves with geometric genus one (2008)
  • Author(s): H. Ishida
  • Organizer: 特異点と多様体の幾何
  • Place of Presentation: 草津セミナーハウス
• [Presentation] Localization of signature of fibered complex surfaces (2007)
  • Author(s): T. Ashikaga
  • Organizer: Japanese-Polish Singularity Conference
  • Place of Presentation: Sopot(Poland)
  • Year and Date: 2007-07-13
• [Presentation] Localization of signature of fibered complex surfaces (2007)
  • Author(s): T. Ashikaga
  • Organizer: Polish-Japanese Singularity Conference, Sopot, POLAND
• [Presentation] 射影直線束内のNon-Galois被覆曲面の標準解消 (2007)
  • Author(s): 足利正
  • Organizer: 分岐被覆に関連する代数幾何とトポロジー(第1回)
  • Place of Presentation: 東北学院大学
• [Presentation] Fixed part of the canonical linear system of a fibred surface (2007)
  • Author(s): K. Konno
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: Universit'a di Padova(Italy)
• [Presentation] Fibred algebraic surfaces and the localization of signature (2007)
  • Author(s): K.Konno
  • Organizer: Geometria em Lisboa
  • Place of Presentation: Instituto Superior Tecnico de Lisboa(Portugal)
• [Presentation] 代数曲線束における相対標準線形系の固定部分について (2007)
  • Author(s): 今野一宏
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
• [Presentation] 射影曲面上の極小な有理関数について (2007)
  • Author(s): 今野一宏
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
• [Presentation] Reducible curves on surfaces (2007)
  • Author(s): 今野一宏
  • Organizer: 高次元代数多様体とベクトル束
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 代数曲面上の有理関数に関する一考察 (2007)
  • Author(s): 今野一宏
  • Organizer: 分岐被覆に関連する代数幾何とトポロジー
  • Place of Presentation: 東北学院大学