• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on CR-approach to the moduli space of toric singularities

Research Project

Project/Area Number 23540099
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKagoshima University

Principal Investigator

MIYAJIMA Kimio  鹿児島大学, 理工学研究科, 教授 (40107850)

Co-Investigator(Kenkyū-buntansha) YOKURA Shoji  鹿児島大学, 大学院・理工学研究科, 教授 (60182680)
AIKOU Tadashi  鹿児島大学, 大学院・理工学研究科, 教授 (00192831)
OBITSU Kunio  鹿児島大学, 大学院・理工学研究科, 准教授 (00325763)
AKAHORI Takao  兵庫県立大学, 大学院・物質理学研究科, 教授 (40117560)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
KeywordsCR構造 / 特異点 / 複素解析幾何 / 変形 / モジュライ
Research Abstract

This research is an application of the deformation theory of strongly pseudo-convex CR structures to the moduli space of normal isolated singularities of complex analytic spaces, that is a new approach rather than a standard algebro-geometric approach to deformation of isolated singularities. The main purpose of this research is to describe a detailed structure of the moduli space of normal isolated singularity germs in terms of deformation of boundary CR structures. In this research, CR description of the Artin deformation of typical cyclic quotient surface singularities are obtained and some related deformation phenomena of isolated singularities are also described from the CR viewpoint. Concerning the moduli of the regular part, a new condition for the vanishing of the second obstruction of deformation of complex structure is found.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (48 results)

All 2014 2013 2012 2011 Other

All Journal Article (14 results) (of which Peer Reviewed: 12 results,  Open Access: 1 results) Presentation (32 results) (of which Invited: 16 results) Book (2 results)

  • [Journal Article] Involutive deforma- tions of the regular part of a nomad surface2014

    • Author(s)
      A. Harris, K. Miyajima
    • Journal Title

      Topics on real and complex singularities (ed. S. Koike et al.)

      Pages: 51-59

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the CR Hamiltonian flows and CR Yamabe problem2014

    • Author(s)
      T. Akahori
    • Journal Title

      Topics on real and complex singularities (ed. S. Koike et al.)

      Pages: 1-12

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Involutive deformations of the regular part of a normal surface2014

    • Author(s)
      Adam Harris and Kimio Miyajima
    • Journal Title

      in "Topics on real and complex singularities (ed. S. Koike et al.)"

      Volume: - Pages: 51-59

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the CR Hamiltonian flows and CR Yamabe problem2014

    • Author(s)
      Takao Akahori
    • Journal Title

      in "Topics on real and complex singularities (ed. S. Koike et al.)"

      Volume: - Pages: 1-12

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Motivic bivariant characteristic classes2014

    • Author(s)
      Joerg Schuermann and Shoji Yokura
    • Journal Title

      Advances in Mathematics

      Volume: 250 Pages: 611-649

    • DOI

      10.1016/j.aim.2013.09.024

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on Rizza-Kahler manifolds2014

    • Author(s)
      Tadashi Aikou
    • Journal Title

      Publ. Math. Debrecen

      Volume: 84 Issue: 1-2 Pages: 105-122

    • DOI

      10.5486/pmd.2014.5801

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characteristic classes of Hilbert schemes od points via symmetrics products2013

    • Author(s)
      S Cappel, L Maxim, T Ohmoto, J Schurmann, S. Yokura
    • Journal Title

      Geometry & Topology

      Volume: 17 Issue: 2 Pages: 1165-1198

    • DOI

      10.2140/gt.2013.17.1165

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recent progress on Takhtajan-Zograf and Weil-Petersson metrics2013

    • Author(s)
      小櫃邦夫
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1862 Pages: 30-41

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Characteristic classes of pro-algebraic varieties and motivic measures2012

    • Author(s)
      Shoji Yokura
    • Journal Title

      Algebraic & Geometric Topology

      Volume: Vol.12 Issue: 1 Pages: 601-641

    • DOI

      10.2140/agt.2012.12.601

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bivariant motivic Hirzebruch class and a zeta function of the motivic Hirzebruch class2012

    • Author(s)
      Shoji Yokura
    • Journal Title

      IRMA Lectures in Mathematics and Theoretical Physics, European Math. Soc.

      Volume: 20 Pages: 285-343

    • DOI

      10.4171/118-1/15

    • ISBN
      9783037191187, 9783037196182
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Averaged Riemannian metrics and connections with application to locally conformal Berwald manifolds2012

    • Author(s)
      Tadashi Aikou
    • Journal Title

      Publ. Math. Debrecen

      Volume: 81 Pages: 179-198

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Grothendieck groups and a categorification of additive invariants(印刷中)2012

    • Author(s)
      Jeorg Schoermann and Shoji Yokura
    • Journal Title

      International Journal of Mathematics

      Volume: 23 Pages: 37-37

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Averaged Riemannian metrics and connections with application to locally conformal Berwald manifolds(印刷中)2012

    • Author(s)
      Tadashi Aikou
    • Journal Title

      Publ. Math. Debrecen

      Volume: 80 Pages: 15-15

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Weil-Petersson 幾何の問題2011

    • Author(s)
      小櫃邦夫
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1731 Pages: 40-51

    • Related Report
      2011 Research-status Report
  • [Presentation] On the CR Hamiltonian flow, I, II2014

    • Author(s)
      赤堀隆夫
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」
    • Place of Presentation
      高知市文化プラザかるぽーと,高知市
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On partially integrable almost CR structures2013

    • Author(s)
      赤堀隆夫
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      コラッセ福島, 福島市
    • Year and Date
      2013-12-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Introduction to s.p.c CR struc- tures and its deformations2013

    • Author(s)
      K. Miyajima
    • Organizer
      Seminar on Functional Analysis and Global Analysis 2013
    • Place of Presentation
      東京理科大学理工学部, 野田市
    • Year and Date
      2013-11-20
    • Related Report
      2013 Final Research Report
  • [Presentation] CR approach to deformation of normal isolated singularities2013

    • Author(s)
      K. Miyajima
    • Organizer
      Australian-Japanese Workshop on Real and Complex Sin- gularities
    • Place of Presentation
      The University of Sydney, Australia
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] On the versal family of CR struc- tures2013

    • Author(s)
      T. Akahori
    • Organizer
      Australian-Japanese Workshop on Real and Complex Singularities
    • Place of Presentation
      The University of Sydney, Australia
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Some remarks on Rizza-Kahler manifolds2013

    • Author(s)
      Tadashi Aikou
    • Organizer
      Colloquium on Differential Geometry abd Its applications
    • Place of Presentation
      Debrecen, Hungary
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A note on complex Finsler metrics on complex vector bundles2013

    • Author(s)
      Tadashi Aikou
    • Organizer
      The 48th Symposium on Finsler Geometry
    • Place of Presentation
      東海大学札幌校舎,札幌市
    • Related Report
      2013 Annual Research Report
  • [Presentation] 強擬凸CR 構造とその変形入門(1), (2)2012

    • Author(s)
      宮嶋公夫
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」
    • Place of Presentation
      鹿児島大学理学部, 鹿児島市
    • Related Report
      2013 Final Research Report
  • [Presentation] 強擬凸CR構造とその変形入門(1)2012

    • Author(s)
      宮嶋公夫
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」(招待講演)
    • Place of Presentation
      鹿児島大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 強擬凸CR構造とその変形入門(2)2012

    • Author(s)
      宮嶋公夫
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」(招待講演)
    • Place of Presentation
      鹿児島大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Scalar curvatures for CR manifolds2012

    • Author(s)
      Takao Akahori
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」(招待講演)
    • Place of Presentation
      鹿児島大学
    • Related Report
      2011 Research-status Report
  • [Presentation] On the CR Hamiltonian flows and CR Yamabe problem (our version)2012

    • Author(s)
      Takao Akahori
    • Organizer
      East Asia Mini-Workshop on CR Geometry(招待講演)
    • Place of Presentation
      Academia Sinica, 台湾
    • Related Report
      2011 Research-status Report
  • [Presentation] On the complex analytic CR-Hamilton flows2011

    • Author(s)
      T. Akahori
    • Organizer
      The 4th Japanese-Australian Workshop on Real and Complex Singularities
    • Place of Presentation
      兵庫教育大学神戸サテライト教室, 神戸市
    • Year and Date
      2011-11-22
    • Related Report
      2013 Final Research Report
  • [Presentation] The deformation theory of CR-structures and the complex analytic CR-Hamiltonian flows2011

    • Author(s)
      Takao Akahori
    • Organizer
      Complex Analysis in Several Variables XIV(招待講演)
    • Place of Presentation
      京都大学
    • Related Report
      2011 Research-status Report
  • [Presentation] On the complex analytic CR-Hamiltonian flows2011

    • Author(s)
      Takao Akahori
    • Organizer
      The 4th Japanese-Australian Workshop on Real and Complex Singularities(招待講演)
    • Place of Presentation
      兵庫教育大学神戸サテライト教室
    • Related Report
      2011 Research-status Report
  • [Presentation] Fiberwise bordism groups2011

    • Author(s)
      Shoji Yokura
    • Organizer
      International Conference "SINGULARITY THEORY CONFERENCE"(招待講演)
    • Place of Presentation
      Univ. of Sci. and Tech. of China Hefei, 中国
    • Related Report
      2011 Research-status Report
  • [Presentation] Some remarks on averaged metrics and connections2011

    • Author(s)
      Tadashi Aikou
    • Organizer
      The 46-th symposium on Finsler Geometry(招待講演)
    • Place of Presentation
      静岡市
    • Related Report
      2011 Research-status Report
  • [Presentation] Takhtajan-Zograf 計量の最近の話題2011

    • Author(s)
      小櫃邦夫
    • Organizer
      リーマン面に関連する位相幾何学(招待講演)
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2011 Research-status Report
  • [Presentation] CR approach to deformation of normal isolated singularities

    • Author(s)
      Kimio Miyajima
    • Organizer
      Australian-Japanese Workshop on Real and Complex Singularities
    • Place of Presentation
      The University of Sydney, Australia
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Introduction to s.p.c CR structures and its deformations

    • Author(s)
      Kimio Miyajima
    • Organizer
      Seminar on Functional Analysis and Global Analysis 2013
    • Place of Presentation
      東京理科大理工学部,野田市
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 孤立特異点の変形へのCRアプローチ

    • Author(s)
      宮嶋公夫
    • Organizer
      第9回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学理学部,鹿児島市
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the versal family of CR structures

    • Author(s)
      Takao Akahori
    • Organizer
      Australian-Japanese Workshop on Real and Complex Singularities
    • Place of Presentation
      The University of Sydney, Australia
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On partially integrable almost CR structure

    • Author(s)
      赤堀隆夫
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      コラッセ福島,福島市
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the partially integrable almost CR structure

    • Author(s)
      赤堀隆夫
    • Organizer
      第9回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Motivic Donaldson-Thomas type Hirzebruch classes

    • Author(s)
      Shoji Yokura
    • Organizer
      The 1st Franco-Japanese-Vietnamese Symposium on Singularities
    • Place of Presentation
      Nice, France
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A motivic Aluffi class

    • Author(s)
      Shoji Yokura
    • Organizer
      One day workshop on hypersurface singularity and its link manifolds
    • Place of Presentation
      東京理科大理学部,東京都
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the CR Yamabe problem

    • Author(s)
      赤堀隆夫
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      東北大学数理科学記念館
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On the CR Yamabe problem

    • Author(s)
      赤堀隆夫
    • Organizer
      研究集会「接触構造,特異点,微分方程式及びその周辺」
    • Place of Presentation
      秋田市カレッジプラザ
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Motivic Hirzebruch class and its zeta function

    • Author(s)
      Shoji Yokura
    • Organizer
      Algebraic Geometry Seminar
    • Place of Presentation
      Courant Institute of Mathematical Sciences, New York University, 米国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Motivic Hirzebruch class and its Donaldson-Thomas type analogue

    • Author(s)
      Shoji Yokura
    • Organizer
      Harvard/MIT Algebraic Geometry Seminar
    • Place of Presentation
      Harvard University, 米国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] オイラー標数とモチビック特性類

    • Author(s)
      與倉昭治
    • Organizer
      2012年度ホモトピー論シンポジウム
    • Place of Presentation
      山口大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Some remarks on Rizza-Kahler amnifolds

    • Author(s)
      Tadashi Aikou
    • Organizer
      47-th Symposium on Finsler Geometry
    • Place of Presentation
      鹿児島市
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] Selected Papers of Masatake Kuranishi2013

    • Author(s)
      Ed. H. Hironaka, T. Akahori, G. Komatsu, K. Miyajima, M. Namba, D. H. Phong, K. Yamaguchi
    • Total Pages
      633
    • Publisher
      World Scientific
    • Related Report
      2013 Final Research Report
  • [Book] CR 多様体, 藤木明編「倉西数学への誘い」2013

    • Author(s)
      宮嶋公夫
    • Publisher
      岩波書店
    • Related Report
      2013 Final Research Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi