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Mixed Hodge structures on log smooth degenerations

Research Project

Project/Area Number 20540054
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Denki University

Principal Investigator

FUJISAWA Taro  Tokyo Denki University, 工学部, 准教授 (60280385)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords混合ホッジ構造 / 対数構造 / 偏極 / 混合ホッジ構 / 対数的ドラームコホモロジー / ウェイトフィルトレーション / ギシン射 / トレース射 / 偏極混合ホッジ構造 / 対数的ホッジ構造
Research Abstract

I succeeded to construct "product" and "the trace map" on the relative log de Rham cohomology groups of a log deformation, which is a typical example of log smooth degeneration. Moreover, I proved that these data provided a polarization on mixed Hodge structures, where the polarization is not a bilinear form on the graded pieces by the weight filtration on the log de Rham cohomology groups, but a bilinear form on the whole log de Rham cohomology groups satisfying the appropriated properties on the graded pieces by the weight filtration.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (4 results)

All 2011 2009 2008

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (3 results)

  • [Journal Article] Polarization on limiting mixed Hodge structures (announcement)2011

    • Author(s)
      藤澤太郎
    • Journal Title

      RIMS Kokyuroku Bessatsu B24

      Pages: 47-66

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] Polarization on the limiting mixed Hodge structure2009

    • Author(s)
      藤澤太郎
    • Organizer
      京都大学数理解析研究所研究集会「高次元代数幾何の周辺」
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-12-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Polarization on the limiting mixed Hodge structure2009

    • Author(s)
      藤澤太郎
    • Organizer
      京大数理解析研究所研究集会「高次元代数幾何の周辺」
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-12-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] Mixed Hodge structures on log smooth degenerations2008

    • Author(s)
      藤澤太郎
    • Organizer
      特異点と多様体の幾何-草津2008-
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2008-09-15
    • Related Report
      2010 Final Research Report 2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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