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Topological Study on the Degeneration Phenomena of Riemann Surfaces

Research Project

Project/Area Number 12440013
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

MATSUMOTO Yukio  The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20011637)

Co-Investigator(Kenkyū-buntansha) IMAYOSHI Yoichi  Osaka City University, Graduate School of Science, Professor, 理学部, 教授 (30091656)
ASHIKAGA Tadashi  Tohoku-Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)
FUKUHARA Shinji  Tsuda College, Department of Mathematics, Professor, 学芸学部, 教授 (20011687)
AHARA Kazushi  Meiji University, School of Science and Technology, Lecturer, 理工学部, 講師 (80247147)
KAWAZUMI Nariya  The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (30214646)
古田 幹雄  東京大学, 大学院・数理科学研究所, 教授 (50181459)
鎌田 聖一  大阪市立大学, 理学部, 助教授 (60254380)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥7,300,000 (Direct Cost: ¥7,300,000)
Fiscal Year 2002: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2001: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2000: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsRiemann surfaces / degeneration / singular fiber / splitting / monodromy / 大域的モノドロミー / クアンドル / 分裂変形 / Seiberg-witten方程式 / 大域モノドロミー / カンドル / 同伴不等式 / 擬周期写像
Research Abstract

During the term of the project, we have made quite a good progress on the problem of splitting a given complicated singular fiber into a number of simpler singular fibers. Among others, we would like to point out Arakawa and Ashikaga's proof of the splittability of hyperelliptic singular fibers and Takamura's research on the construction of splitting families for not necessarily hyperelliptic singular fibers, Takamura being a cooperative researcher. An experimental method is also very important to the study of splitting of singular fibers. In fact Ahara developed a software "Splitica" by which we can observe the splitting motion of "star-shaped" singular fibers on a computer display. As for the global study of monodromy, Imayoshi, Ito, and Yamamoto made a research from function theoretic viewpoint. Also the quandle of cords which might be important to the study of Lefschetz fibrations, Kamada and Matsumoto studied their algebraic representation. There are obtained many other related results.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] T.Ashikaga: "Classification of degenerations of curves of genus 3 via Matsumoto-Montesinos' theorem"Tohoku Math.J.. 54. 195-226 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Fukuhara: "Dedekind symbols associated with J-forms and their reciprocity law"J.Number Theory. 98. 236-253 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Fukuhara: "Non-Commutative polynomial reciprocity formulae"International J.Math.. 12. 973-986 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Ahara: "Conjugacy classes of hyperbolic mapping class group of genus 2 and 3"Experimental mathematics. 9. 383-396 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N.Kawazumi: "Weierstrass points and Morita-Mumford classes on hyper elliptic mapping class groups"Topology and its appl.. 125. 363-383 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Kamada: "Wirtinger presentations for higher dimensional manifold knots obtained from diagrams"Fund.Math.. 168. 105-112 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Ashikaga et al.: "Classification of degenerations of curves of genus 3 via Matsumoto-Montesinos theorem"Tohoku Math. J.. 54. 195-226 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Fukuhara: "Dedekind symbols associated with J-forms and their reciprocity law"J.Number Theory. 98. 236-253 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Fukuhara et al.: "Non-commutative polynomial reciprocity formulae"Intern. J. Math.. 12. 973-986 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Ahara: "Conjugacy classes of hyperbolic mapping class group of genus 2 and 3"Experimental math.. 9. 383-396 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] N.Kawazumi: "Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups"Topology its appl.. 125. 363-383 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Kamada: "Wirtinger presentation for higher dimensional manifold knots obtained from diagrams"Fund. Math.. 168. 105-112 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Ashikaga: "Classifications of degenerations of curves of genus 3 via Matsumoto-Montesinos' theorem"Tohoku Math. J.. 54. 195-226 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Fukuhara: "Dedekind Symbols associated with J-forms and their reciprocity law"J. Number Theory. 98. 236-253 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Fukuhara: "Non-commutative polynomial reciprocity formulae"International J. Math.. 12. 973-986 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Ahara: "Conjugacy classes of hyperbolic mapping class group of genus 2 and 3"Experimental mathematics. 9. 383-396 (2000)

    • Related Report
      2002 Annual Research Report
  • [Publications] N.Kawazumi: "Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups"Topology and its appl.. 125. 363-383 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Kamada: "Wirtinger presentations for higher dimensional manifold knots obtained from diagrams"Fund. Math.. 168. 105-112 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Furuta: "Monopole equation and the 11/8-conjecture"Mathematical Research Letters. 8. 279-291 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Furuta: "Spin 4-manifolds with Signature=-32"Mathematical Research Letters. 8. 293-301 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Kamada: "Wirtinger presentations for higher dimensional manifold knots"Fund. Math. 168. 105-112 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] N.Kawazumi: "Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups"Topology and its appl. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Arakawa: "Local splitting families of hyperelliptic pencils, I"Tohoku Math. J. 53. 369-394 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Fukuhara: "Non-commutative polynomial resiprocity formulae"Internat. J. Math.. 12. 973-986 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 今吉洋一(訳): "ヴィジュアル複素解析"培風館. 662 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Kamada: "Certain racks associated with the braid groups"Proc.Int.Conf.on Knot Theory "Knots in Hellas". 118-130 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Fukuhara: "Twisted generalized Dedekind symbols"J.Number Theory. 82. 47-68 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Imayoshi: "The Nielsen-Thurston-Bers Type of elements of the monodromy group of a holomorphic family of Riemann sufaces induced by a kodaira surface"Lecture Notes in Pure and Applied Math.. 214. 169-177 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Kawazumi: "The meromorphic solutions of the Bruschi-Calogero eq."Publ.RIMS.Kyoto Univ.. 36. 85-109 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] J.S.Carter: "State-sum invariants of knotted curves and surfaces from quandle cohomology"Electron.Res.Announc.Amer.Math.Soc.. 5. 146-156 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Ahara: "Conjugacy Classes of the Hyperelliptic Mapping Class Groups of Genus 2 and 3"Experimental Meth.,. 9. 383-396 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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