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A study on mixed Hodge structures on the relative log de Rham cohomology groups of log smooth degenerations

Research Project

Project/Area Number 18540060
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagano National College of Technology

Principal Investigator

FUJISAWA Taro  Nagano National College of Technology, dep. of general education, associate prof. (60280385)

Project Period (FY) 2006 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥1,480,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Keywordsmixed Hodge structure / weight filtrations / logarithmic structures / ウエイト・フィルトレーション / リーマン・ヒルベルト対応
Research Abstract

In 2006, I studied the case of semi-stable degeneration of compact Kahler complex manifolds, as an important example of log smooth degenerations. In particular, weight filtrations on the mixed Hodge complexes constructed on the singular fibers were considered deeply. I found that the properties of these weight filtrations were related to the properties of monodromy logarithms
In 2007, I have been studying these weight filtrations and found that the monodromy logarithms played important roles to construct the weight filtrations for the case of log smooth degenerations.
The monodromy action on the cohomology groups is quasi-unipotent in general. However I expect that we can construct mixed Hodge complexes, for the case of log smooth degeneration, by the reduction to the case where the monodromy actions are unipotent, once I find out the appropriate conditions which assures the unipotency of the monodromy.
In order to find out such conditions, I calculated the cohomology sheaves of the relative log de Rham complexes for log smooth degenerations.

Report

(3 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • Research Products

    (4 results)

All 2008 2006

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (2 results)

  • [Journal Article] Mixed Hodge structures on log smooth degenerations2008

    • Author(s)
      Taro Fujisawa
    • Journal Title

      Tohoku Mathematical Journal 60

      Pages: 71-100

    • NAID

      110006602741

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Mixed Hodge structures on log smooth degenerations2008

    • Author(s)
      Taro Fujisawa
    • Journal Title

      Tohoku Mathematical Journal(refereed) Vol.60

      Pages: 71-100

    • NAID

      110006602741

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Weight filtrations on limits of Hodge structures2006

    • Author(s)
      藤澤 太郎
    • Organizer
      Log mixed Hodge theory and its geometric applications
    • Place of Presentation
      大阪大学理学部
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Weight filtrations on limits of Hodge structures2006

    • Author(s)
      Taro Fujisawa
    • Organizer
      Log mixed Hodge theory and its geometric applications
    • Place of Presentation
      Osaka University
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2006-04-01   Modified: 2016-04-21  

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