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Moduli of representations and related topics (2)

Research Project

Project/Area Number 23540044
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Yamanashi

Principal Investigator

NAKAMOTO Kazunori  山梨大学, 総合研究部, 教授 (30342570)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords代数学 / 代数幾何学 / 不変式論 / 表現のモジュライ
Outline of Final Research Achievements

The paper on the construction of the moduli of representations with Borel mold has been published. As preprints, we announced the results on the construction of the moduli of representations of degree 2 for each mold and on topological properties of them for free monoids (joint work with Takeshi Torii(Okayama University)). We completed the classification on thick representations and dense representations of complex simple Lie groups (joint work with Yasuhiro Omoda (Akashi National College of Technology)). As a joint work with Takeshi Torii, we also see that the stratification of the moduli of representations with respect to Loewy series is much related with whether the moduli is polynomial count, and that each stratification is locally closed in the representation variety over any algebraically closed field.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (12 results)

All 2014 2013 2012 2011 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (3 results) Remarks (5 results)

  • [Journal Article] The moduli of representations with Borel mold2014

    • Author(s)
      Kazunori Nakamoto
    • Journal Title

      International Journal of Mathematics

      Volume: 25 Issue: 07 Pages: 1450067-1450067

    • DOI

      10.1142/s0129167x14500670

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A new construction of \tilde{D}_5-singularities and generalization of Slodowy slices2013

    • Author(s)
      Kazunori Nakamoto and Meral Tosun
    • Journal Title

      Journal of Algebra

      Volume: 376 Pages: 139-151

    • DOI

      10.1016/j.jalgebra.2012.11.016

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Rational homotopy type of the moduli of representations with Borel mold2012

    • Author(s)
      Kazunori Nakamoto and Takeshi Torii
    • Journal Title

      Forum Mathematicum

      Volume: 24 Issue: 3 Pages: 507-538

    • DOI

      10.1515/form.2011.071

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Topology of the representation varieties with Borel mold for unstable cases2011

    • Author(s)
      Kazunori Nakamoto and Takeshi Torii
    • Journal Title

      Journal of the Australian Mathematical Society

      Volume: 91 Pages: 55-87

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] The moduli of absolutely thick representations2012

    • Author(s)
      Kazunori Nakamoto
    • Organizer
      Workshop and International Conference on Representations of Algebras (ICRA 2012)
    • Place of Presentation
      ビーレフェルト大学(ドイツ)
    • Related Report
      2012 Research-status Report
  • [Presentation] Topics on the moduli of representations of degree 22011

    • Author(s)
      Kazunori Nakamoto
    • Organizer
      第6回日中韓環論国際シンポジューム
    • Place of Presentation
      Kyung Hee大学(韓国)
    • Related Report
      2011 Research-status Report
  • [Presentation] Virtual Hodge polynomials of the moduli spaces of representations for free monoids

    • Author(s)
      中本 和典
    • Organizer
      代数幾何学城崎シンポジウム
    • Place of Presentation
      城崎大会議館(兵庫県豊岡市城崎町)
    • Related Report
      2013 Research-status Report
  • [Remarks] 山梨大学 研究者総覧 研究者公開情報

    • URL

      http://erdb.yamanashi.ac.jp/rdb/A_DispInfo.Scholar?ID=D064338FEDDFC538

    • Related Report
      2014 Annual Research Report
  • [Remarks] 山梨大学医学部 医学教育センター(数学)

    • URL

      http://www.med.yamanashi.ac.jp/medicine/mathematics/

    • Related Report
      2014 Annual Research Report
  • [Remarks] 山梨大学 研究者総覧 研究者公開情報

    • URL

      http://erdb.yamanashi.ac.jp/rdb/A_DispInfo.Scholar?ID=D064338FEDDFC538

    • Related Report
      2013 Research-status Report
  • [Remarks] 山梨大学 研究者総覧 研究者公開情報

    • URL

      http://erdb.yamanashi.ac.jp/rdb/A_DispInfo.Scholar/9/D064338FEDDFC538.html

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://erdb.yamanashi.ac.jp/rdb/A_DispInfo.Scholar/9/D064338FEDDFC538.html

    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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