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Geometry on real closed fields and sevaral complex variable functions

Research Project

Project/Area Number 22540076
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNagoya University

Principal Investigator

SHIOTA Masahiro  名古屋大学, 多元数理科学研究科, 名誉教授 (00027385)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords位相幾何 / 計算可能性 / 幾何学
Research Abstract

I worked with Fichou of University of Rennes on two problems. One problem is an open problem of singularity theory on classifications of analytic function germs, and the other is about Milnor fibers. The first was already published in a journal, and we are writing the second.
I worked with Tressl of Manchester Universuty. We solved a well known problem on a topological version of Artin approximation theorem. We are now writing it.
I also worked with Koike of Hyogo University of education and Fukui of Saitama University. We solved two problems on real singularity theory. One was published, and the other will be written.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (23 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (7 results) (of which Invited: 2 results)

  • [Journal Article] O-minimal Hauptvermutung for polyhedra I2014

    • Author(s)
      塩田昌弘
    • Journal Title

      Invent. Math.

      Volume: 196巻 Pages: 163-232

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] O-minimal Hauptvermutung for polyhedra I2014

    • Author(s)
      Shiota
    • Journal Title

      Invent. math.

      Volume: 196 Issue: 1 Pages: 163-232

    • DOI

      10.1007/s00222-013-0467-y

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Triangulation of the map of a G-manifold to its orbit2013

    • Author(s)
      塩田昌弘, 村山充孝
    • Journal Title

      Nagoya Math. J.

      Volume: 212巻 Pages: 159-195

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Directional properties of the sets definable in o-minimal structure2013

    • Author(s)
      塩田昌弘, L. Paunescu, 小池敏司, TaLe Loi
    • Journal Title

      Annales de l'Institute Fourier

      Volume: 63巻 Pages: 2017-2047

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Virtual Poincare polynomial of the link of a real algebraic variety2013

    • Author(s)
      塩田昌弘, Goulwen Fichou
    • Journal Title

      Math. Zeitschrift

      Volume: 273巻 Pages: 1053-1061

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Virtual Poincare polynomial of the link of a real algebraic variety2013

    • Author(s)
      Fichou, Shiota
    • Journal Title

      Math. Zeitschrift

      Volume: 273 Pages: 1053-1061

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Directional properties of the sets definable in o-minimal structure2013

    • Author(s)
      Paunescu, Koike, TaLe Loi, Shiota
    • Journal Title

      Annales de l'Institute Fourier

      Volume: 63 Pages: 2017-2047

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Triangulation of the map of a G-manifold to its orbit space2013

    • Author(s)
      Murayama, Shiota
    • Journal Title

      Nagoya Math. J.

      Volume: 212 Pages: 159-195

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Virtual Poincare polynomial of the link of a real algebraic variety2013

    • Author(s)
      G.Fichou
    • Journal Title

      Math. Zeitschrift

      Volume: 273 Pages: 1053-1061

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Directional properties of the sets definable in o-minimal structure2013

    • Author(s)
      S. Koike
    • Journal Title

      Annales de l'Institute Fourier

      Volume: 63

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic equivalence of normal crossing functions on a real analytic manifold2012

    • Author(s)
      塩田昌弘, Goulwen Fichou
    • Journal Title

      Proceedings of London Math. Soc.

      Volume: 104巻 Pages: 1121-1170

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic equivalence of normal crossing functions on a real analytic manifold2012

    • Author(s)
      G.Fichou
    • Journal Title

      Proceedings of London Math. Soc

      Volume: 104 Pages: 1121-1170

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On almost Blow-analytic equivalence2011

    • Author(s)
      塩田昌弘, Goulwen Fichou
    • Journal Title

      Proceedings of London Math. Soc.

      Volume: 103巻 Pages: 676-709

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On almost Blow-analytic equivalence2011

    • Author(s)
      Goulwen Fichou, Masahiro Shiota
    • Journal Title

      Pro.London Math.Soc.

      Volume: 103 Pages: 676-709

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic and Nash equivalence of Nash maps2010

    • Author(s)
      塩田昌弘
    • Journal Title

      Bull. London Math. Soc.

      Volume: 42巻 Pages: 1055-1064

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic and Nash equivalence of Nash maps2010

    • Author(s)
      Shiota Masahiro
    • Journal Title

      Bull. London Math. Soc.

      Volume: 42 Pages: 1055-1064

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] An application to G-manifold problem2013

    • Author(s)
      塩田昌弘
    • Organizer
      Workshop Applications of 0-minimality to analysis and number theory
    • Place of Presentation
      ドイツ, パッサウ大学
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Semialgebraic singularity theory2012

    • Author(s)
      塩田昌弘
    • Organizer
      Geometry and topology of singularity spaces
    • Place of Presentation
      フランス, マルセイユ
    • Year and Date
      2012-10-01
    • Related Report
      2013 Final Research Report
  • [Presentation] How to avoid integration in singularity theory2011

    • Author(s)
      塩田昌弘
    • Organizer
      Symposium on 0-minimal structure
    • Place of Presentation
      カナダ, トロント大学
    • Year and Date
      2011-08-06
    • Related Report
      2013 Final Research Report
  • [Presentation] How to avoid integration in singularity theory2011

    • Author(s)
      Masahiro Shiota
    • Organizer
      Symposium on 0-minimal structure
    • Place of Presentation
      カナダトロント大学(招待講演)
    • Year and Date
      2011-08-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Analytic and Nash equivalence of Nash maps2010

    • Author(s)
      塩田昌弘
    • Organizer
      空間認識のための特異点理論研究集会
    • Place of Presentation
      伊勢観光文化会館
    • Year and Date
      2010-06-03
    • Related Report
      2013 Final Research Report 2010 Annual Research Report
  • [Presentation] An application to G-manifold problem

    • Author(s)
      Shiota
    • Organizer
      Workshop Applications of O-Minimality to Analysis and Number Theory
    • Place of Presentation
      ドイツPassau
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Semialgebraic singularity theory

    • Author(s)
      M. Shiota
    • Organizer
      Geometry and topology of singularity spaces
    • Place of Presentation
      Marseille France
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2010-08-23   Modified: 2019-07-29  

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