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Resolution of singularities by using Newton polyhedra and its application to analysis

Research Project

Project/Area Number 15K04932
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

Kamimoto Joe  九州大学, 数理学研究院, 准教授 (90301374)

Project Period (FY) 2015-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsニュートン多面体 / 特異点解消定理 / ベルグマン核 / ダンジェロの型 / 代数曲線 / 振動積分 / 局所ゼータ関数 / 特異点解消 / 接触位数 / ニュートン非退化 / 実超曲面 / 有限型 / 有限型領域 / ピーク関数
Outline of Final Research Achievements

By using Newton polyhedra, which is an important concept in singularity theory,
we developed a quantitative resolution of singularities theorem. Furthermore, we apply the resolution theorem to several complex variables and harmonic analysis and obtain many kinds of interesting results. To be more specific, we obtain strong results about the analytic continuation of local zeta functions, asymptotic analysis of oscillatory integrals and determination of D'Angelo's types.

Academic Significance and Societal Importance of the Research Achievements

代数や幾何における重要な成果をさらに発展させ応用することにより、今までに十分でなかった解析学における重要な問題について、多くの成果を得たこと。

Report

(7 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (37 results)

All 2021 2020 2019 2018 2017 2016 2015

All Journal Article (18 results) (of which Peer Reviewed: 12 results,  Open Access: 13 results,  Acknowledgement Compliant: 3 results) Presentation (19 results) (of which Int'l Joint Research: 3 results,  Invited: 15 results)

  • [Journal Article] Newton polyhedra and order of contact on real hypersurfaces2021

    • Author(s)
      KAMIMOTO Joe
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 73 Issue: 1 Pages: 1-39

    • DOI

      10.2969/jmsj/80868086

    • NAID

      130007973712

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On Holomorphic Curves Tangent to Real Hypersurfaces of Infinite Type2020

    • Author(s)
      Kamimoto Joe
    • Journal Title

      The Journal of Geometric Analysis

      Volume: - Issue: 8 Pages: 1-17

    • DOI

      10.1007/s12220-020-00567-z

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Meromorphy of local zeta functions in smooth model cases2020

    • Author(s)
      Kamimoto Joe、Nose Toshihiro
    • Journal Title

      Journal of Functional Analysis

      Volume: 278 Issue: 6 Pages: 108408-108408

    • DOI

      10.1016/j.jfa.2019.108408

    • Related Report
      2020 Annual Research Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Newton polyhedra and order of contact on real hypersurfaces2020

    • Author(s)
      Kamimoto Joe
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A sufficient condition for equality of regular type and singular type of real hypersurfaces2020

    • Author(s)
      Kamimoto Joe
    • Journal Title

      数理解析研究所講究録

      Volume: 未定

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Nonpolar singularities of local zeta functions in some smooth case2019

    • Author(s)
      Kamimoto Joe、Nose Toshihiro
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 372 Issue: 1 Pages: 661-676

    • DOI

      10.1090/tran/7771

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Nonpolar singularities of local zeta functions in some smooth case2019

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A sufficient condition for equality of regular type and singular type fo real hypersurfaces2019

    • Author(s)
      Joe Kamimoto
    • Journal Title

      数理解析研究所講究録

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Non-polar singularities of local zeta functions in some smooth case2018

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: To appear

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic limit of oscillatory integrals with certain smooth phases,2017

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B63 Pages: 101-112

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic limit of oscillatory integrals with certain smooth phases2017

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      RIMS K\^oky\^uroku Bessatsu

      Volume: 63 Pages: 101-112

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Toric resolution of singularities in a certain class of $C^{\infty}$ functions and asymptotic analysis of oscillatory integrals,2016

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      J. Math. Soc. Univ. Tokyo

      Volume: 23 Pages: 425-485

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Newton polyhedra and weighted oscillatory integrals with smooth phases2016

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 368 Pages: 5301-5361

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On asymptotic expansions of oscillatory integrals with smooth phase in two dimensions2016

    • Author(s)
      J. Kamimoto and T. Nose
    • Journal Title

      RIMS K\^oky\^uroku Bessatsu

      Volume: B57 Pages: 141-157

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Toric resolution of singularities in a certain class of $C^{\infty}$ functions and asymptotic analysis of oscillatory integrals2016

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      J. Math. Soc. Univ. Tokyo

      Volume: 23

    • Related Report
      2015 Research-status Report
  • [Journal Article] Newton polyhedra and weighted oscillatory integrals with smooth phases2016

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 368

    • Related Report
      2015 Research-status Report
  • [Journal Article] On asymptotic expansions of oscillatory integrals with smooth phase in two dimensions2016

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      RIMS K\^oky\^uroku Bessatsu

      Volume: 未定

    • Related Report
      2015 Research-status Report
  • [Journal Article] On meromorphic continuation of local zeta functions2015

    • Author(s)
      Joe Kamimoto and Toshihiro Nose
    • Journal Title

      Proceedings of KSCV10, F. Bracci et al. (eds.)

      Volume: 144

    • Related Report
      2015 Research-status Report
  • [Presentation] Asymptotic analysis of oscillatory integrals with degenerate phases2021

    • Author(s)
      Joe Kamimoto
    • Organizer
      偏微分方程式姫路研究集会
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] C^∞ 平面曲線の特異点解消と局所ゼータ関数の有理型解析接続2020

    • Author(s)
      神本 丈
    • Organizer
      第63回函数論シンポジウム
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On holomorphic curves tangent to real hypersurfaces of infinite type2020

    • Author(s)
      神本 丈
    • Organizer
      多変数関数論冬セミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On meromorphy of local zeta functions2020

    • Author(s)
      Kamimoto Joe
    • Organizer
      研究集会「第15回代数・解析・幾何学セミナー」, 鹿児島大学
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 局所ゼータ関数の有理型解析接続可能領域について2020

    • Author(s)
      神本丈,  野瀬敏洋
    • Organizer
      日本数学会2020年度春季総合分科会,日本大学
    • Related Report
      2019 Research-status Report
  • [Presentation] 無限型擬凸領域のベルグマン核の境界挙動2019

    • Author(s)
      神本 丈
    • Organizer
      第54回函数論サマーセミナー,静岡県伊豆の国市
    • Related Report
      2019 Research-status Report
  • [Presentation] 多変数関数論におけるニュートン多面体とその応用2019

    • Author(s)
      神本 丈
    • Organizer
      日本数学会2019年度秋季総合分科会,特別講演, 金沢大学
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Meromorphy of local zeta functions in smooth model cases2019

    • Author(s)
      Kamimoto Joe
    • Organizer
      研究集会「超局所解析と漸近解析」, 京大数理解析研究所
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] ニュートン多面体と振動積分の漸近解析 I, II2019

    • Author(s)
      神本 丈
    • Organizer
      筑波RCMS解析学シンポジウム
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Regular and singular orders of contact on real hypersurfaces.2018

    • Author(s)
      神本 丈
    • Organizer
      第53回函数論サマーセミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Non-polar singularities of local zeta functions in smooth cases.2018

    • Author(s)
      神本 丈
    • Organizer
      日本数学会2018年秋季総合分科会、岡山大学
    • Related Report
      2018 Research-status Report
  • [Presentation] Regular and singular orders of contact on real hypersurfaces.2018

    • Author(s)
      神本 丈
    • Organizer
      代数解析学の諸問題ー超局所解析及び漸近解析ー、京大数理解析
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] ニュートン多面体と重みつき振動積分2018

    • Author(s)
      神本 丈
    • Organizer
      第228回 広島数理解析セミナー、広島大学
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Newton polyhedra and order of contact on real hypersurfaces.2018

    • Author(s)
      神本 丈
    • Organizer
      複素解析幾何セミナー、東京大学
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] ニュートン多面体を用いた特異点解消とその解析学への応用2018

    • Author(s)
      神本 丈
    • Organizer
      研究集会「接触構造、特異点、微分方程式及びその周辺」 金沢市,
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] ベルグマン核の漸近解析, 2017年9月6日.2017

    • Author(s)
      神本 丈
    • Organizer
      第52回函数論サマーセミナー,福岡県柳川市,
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Failure of meromorphy for local zeta functions,2017

    • Author(s)
      Joe Kamimoto
    • Organizer
      RIMS 共同研究 (公開型)「超局所解析と漸近解析」 京大数理解析研
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On analytic continuation of local zeta functions2016

    • Author(s)
      Joe Kamimoto
    • Organizer
      研究集会「New development of microlocal analysis and singular perturbation theory」
    • Place of Presentation
      京大数理解析研
    • Year and Date
      2016-10-03
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic analysis of oscillatory integrals and local zeta functions2015

    • Author(s)
      神本 丈
    • Organizer
      研究集会「保存則をもつ偏微分方程式に対する解の正則性・特異性の研究」
    • Place of Presentation
      京大数理解析研究所
    • Year and Date
      2015-06-03
    • Related Report
      2015 Research-status Report
    • Invited

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Published: 2015-04-16   Modified: 2022-01-27  

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