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Deformation theory of complex structures on solvmanifolds

Research Project

Project/Area Number 25887019
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo Institute of Technology

Principal Investigator

KASUYA Hisashi  東京工業大学, 理工学研究科, 助教 (80712611)

Project Period (FY) 2013-08-30 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords可解多様体 / 変形理論 / Hodge理論 / 局所系 / 局所系コホモロジー / ホッジ理論 / 佐々木構造 / deldelbar-Lemma
Outline of Final Research Achievements

We obtain many results on relations between geometry of solvmanifolds and deformations of complex structures. In particular, we obtain counterexamples for closedness of Hodge decomposition. Moreover, we obtain many results on the Hodge theory of local system cohomology. In view of Kahler geometry, these results are surprising. Non-Kahler geometry had not been studied very much. By these results, we can give interests in Non-Kahler geometry.

Report

(3 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • Research Products

    (16 results)

All 2015 2014 2013

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 2 results,  Acknowledgement Compliant: 4 results) Presentation (9 results) (of which Invited: 9 results)

  • [Journal Article] Flat bundles and Hyper-Hodge decomposition on solvmanifolds2015

    • Author(s)
      Hisashi Kasuya
    • Journal Title

      International Mathematics Research Notices

      Volume: 未定 Issue: 19 Pages: 9638-9659

    • DOI

      10.1093/imrn/rnu244

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Cohomologies of deformations of solvmanifolds and closedness of some properties2015

    • Author(s)
      Daniele Angella and Hisashi Kasuya
    • Journal Title

      Mathematica Universalis

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Hodge theory for twisted differentials2014

    • Author(s)
      Daniele Angella and Hisashi Kasuya
    • Journal Title

      Complex manifolds

      Volume: 1 Issue: 1

    • DOI

      10.2478/coma-2014-0005

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Examples of non-Kahler solvmanifolds admitting hodge decomposition2014

    • Author(s)
      Hisashi Kasuya
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 106

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] de Rham and Dolbeault Cohomology of solvmanifolds with local systems2014

    • Author(s)
      糟谷 久矢
    • Journal Title

      Mathematical Research Letters

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] SKT and tamed symplectic structures on solvmanifolds.2014

    • Author(s)
      Anna Fino, 糟谷久矢, Luigi Vezzoni
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 未定

    • NAID

      130007961970

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lefschetz coincidence numbers of solvmanifolds with Mostow conditions2014

    • Author(s)
      糟谷 久矢
    • Journal Title

      Archivum Mathematicum

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] Computations of Lefschetz numbers of solvmanifolds and polycyclic groups2014

    • Author(s)
      Hisashi Kasuya
    • Organizer
      Topological Fixed Point Theory and Related Topics
    • Place of Presentation
      Poznan
    • Year and Date
      2014-09-17 – 2014-09-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Examples of solvmanifolds admitting Hodge decomposition but no K"ahler structure2014

    • Author(s)
      Hisashi Kasuya
    • Organizer
      ICM 2014 Satellite Conference on Real & Complex Submanifold
    • Place of Presentation
      Daejeon
    • Year and Date
      2014-08-10 – 2014-08-12
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Hodge decomposition on solvmanifolds2014

    • Author(s)
      Hisashi Kasuya
    • Organizer
      9th Pacific Rim Conference on Complex Geometry -A satellite conference of ICM2014-
    • Place of Presentation
      Gunsan
    • Year and Date
      2014-07-27 – 2014-08-01
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Hodge theory on solvmanifolds2014

    • Author(s)
      Hisashi Kasuya
    • Organizer
      Complex Geometry and Lie Groups
    • Place of Presentation
      Torino
    • Year and Date
      2014-06-16 – 2014-06-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Central theorems for cohomologies of certain solvable groups2014

    • Author(s)
      Hisashi Kasuya
    • Organizer
      Discrete Groups and Geometric Structures
    • Place of Presentation
      Leuven
    • Year and Date
      2014-06-02 – 2014-06-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Central theorems for cohomologies of certain solvable groups2014

    • Author(s)
      糟谷久矢
    • Organizer
      第9回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Differential Gerstenhaber algebras and generalized deformations of solvmanifolds2014

    • Author(s)
      糟谷久矢
    • Organizer
      Progress of geometric structures on manifolds
    • Place of Presentation
      名城大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Cohomologies and deformations of solvmanifolds2013

    • Author(s)
      糟谷久矢
    • Organizer
      日本数学会2013年度秋季総合分科会特別講演
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Cohomologies of deformations of solvmanifolds and closedness of some properties2013

    • Author(s)
      糟谷久矢
    • Organizer
      第19回複素幾何シンポジウム
    • Place of Presentation
      信州菅平高原 プチホテル ゾンタック
    • Related Report
      2013 Annual Research Report
    • Invited

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Published: 2013-09-12   Modified: 2019-07-29  

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