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2016 Fiscal Year Annual Research Report

Comprehensive study of geometric complex analysis

Research Project

Project/Area Number 15H02057
Research InstitutionThe University of Tokyo

Principal Investigator

平地 健吾  東京大学, 大学院数理科学研究科, 教授 (60218790)

Project Period (FY) 2015-04-01 – 2020-03-31
Keywords多変数函数論 / L2拡張定理 / 双有理幾何学 / 特異点論 / ツイスター空間 / CR幾何学 / ベルグマン核
Outline of Annual Research Achievements

7月には国際会議「多変数複素解析葉山シンポジウム」8月には「函数論シンポジウム」9月には若手研究者の中心とした「函数論サマーセミナー」を開催し研究成果発表を行った.東京大学では毎週複素解析幾何セミナーを実施した.
平地は変形複体を用いてCR構造のモジュライ空間を研究し球面の剛性定理へ応用した.大沢健夫は最良定数つきのL2拡張定理の新しい定式化を与えるとともに,Bargmann-Fock空間における拡張定理を示した.高山茂晴は複素多様体間の射影的な射fの一点でのファイバーX_0の退化の様子を研究し,fの双有理モデルの取り換えにより,X_0の特異性が緩やかであるようにできるための条件を多重種数のある等式として与えた.松村慎一は双有理幾何学に現れるLC特異点で機能する単射性定理を研究し,LCよりマイルドなPLT特異点で機能する単射性定理を得た. 本多宣博は代数的なツイスター空間の構造解析を行い,反標準系の半分がペンシルになっているとき,その何倍かがある単純な構造を持った有理多様体への二重被覆写像を引き起こすことを示した.吉川謙一はアーベル的3次元カラビ・ヤウ軌道体に対するBCOV不変量を二通りの方法で構成し,それらが充たす微分方程式を決定した.神本丈は特異点論において重要な概念であるニュートン多面体のテクニックを調和解析および多変数複素解析の問題に応用した.奥間智弘は具体的な特異点の位相型を固定して幾何種数などの基本的な不変量の値域を決定し,楕円型特異点について正規化された節減数およびイデアルのコホモロジーの次元の値域を決定した.伊師英之は多変量解析における指数型分布族と多変数函数論における再生核ヒルベルト空間の理論の関係について基礎的な考察を行った.辻元は有界擬凸領域上の擬凸族のベルグマン核についての不等式を導いた.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

予定通りに国際会議及び国内向けの研究集会が開催され盛んに研究成果発表と研究者の交流が行われている.各個人の研究も研究実績にあるように滞りなく進んでいる.

Strategy for Future Research Activity

7月には国際会議「多変数複素解析葉山シンポジウム」(代表:吉川謙一)を開催する. 9月には若手研究者の中心とした「函数論サマーセミナー」(代表:野瀬敏洋)また冬には国内の研究成果発表の場として「函数論シンポジウム」を開催し(代表:松本和子)当該分野の相互理解をはかる.東京大学では毎週セミナーを実施し,研究者間の情報の共有をはかる.今年度は野村亮介氏(特任研究員)がセミナーの実務的な運営を行う.

  • Research Products

    (45 results)

All 2017 2016

All Journal Article (17 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 17 results,  Acknowledgement Compliant: 2 results) Presentation (27 results) (of which Int'l Joint Research: 14 results,  Invited: 26 results) Funded Workshop (1 results)

  • [Journal Article] Bergman kernel function for Hartogs domains over bounded homogeneous domains2017

    • Author(s)
      H. Ishi,J.-D. Park and A. Yamamori
    • Journal Title

      J. Geom. Anal.

      Volume: 27 Pages: 1703--1736

    • Peer Reviewed
  • [Journal Article] Rees algebras and $p_g$-ideals in a two-dimensional normal local domain2017

    • Author(s)
      T. Okuma,K. Watanabe and K. Yoshida
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 145 Pages: 39--47

    • DOI

      http://dx.doi.org/10.1090/proc/13235

    • Peer Reviewed
  • [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: B63 Pages: 101--112

    • Peer Reviewed
  • [Journal Article] Resultants and the Borcherds Φ-function2017

    • Author(s)
      S. Kawaguchi,S. Mukai,K.-I. Yoshikawa
    • Journal Title

      American Journal of Mathematics

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed
  • [Journal Article] Analytic torsion for Borcea-Voisin threefolds2017

    • Author(s)
      K.-I. Yoshikawa
    • Journal Title

      Progress in Mathathematics

      Volume: 310 Pages: 279-361

    • Peer Reviewed
  • [Journal Article] Algebraic dimension of twistor spaces whose fundamental system is a pencil2017

    • Author(s)
      N. Honda and B. Kreussler
    • Journal Title

      J. London Math. Soc.

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles2017

    • Author(s)
      S. Alexakis and K. Hirachi
    • Journal Title

      Adv. Math.

      Volume: 308 Pages: 348--403

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Variation of total Q-prime curvature on CR manifolds2017

    • Author(s)
      K. Hirachi,T. Marugame,Y. Matsumoto
    • Journal Title

      Adv. Math.

      Volume: 306 Pages: 1333--1376

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the extension of L^2 holomorphic functions VII; Hypersurfaces with isolated singularities2017

    • Author(s)
      T. Ohsawa
    • Journal Title

      Science China Mathematics

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed
  • [Journal Article] On the extension of L^2 holomorphic functions VIII; a remark on a theorem of Guan and Zhou2017

    • Author(s)
      T. Ohsawa
    • Journal Title

      Intern. J. Math.

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed
  • [Journal Article] Effective degree bounds for generalized Gauss map images2017

    • Author(s)
      G. Heier and S. Takayama
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed
  • [Journal Article] Versions of injectivity and extension theorems2017

    • Author(s)
      S. Matsumura
    • Journal Title

      Journal of Algebraic Geometry

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed
  • [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

    • Peer Reviewed
  • [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

    • Peer Reviewed
  • [Journal Article] Unobstructed deformations of generalized complex structures induced by $C^{\infty}$ logarithmic symplectic structures and logarithmic Poisson structures2016

    • Author(s)
      R. Goto
    • Journal Title

      Geometry and topology of manifolds, Springer Proc. Math. Stat.

      Volume: 154 Pages: 159-183

    • Peer Reviewed
  • [Journal Article] $C^{\infty}$-logarithmic transformations and generalized complex structures2016

    • Author(s)
      R. Goto and K Hayano
    • Journal Title

      J. Symplectic Geom.

      Volume: 14 Pages: 341-357

    • Peer Reviewed
  • [Journal Article] 対合付きK3曲面と解析的捩率2016

    • Author(s)
      吉川 謙一
    • Journal Title

      数学

      Volume: 68 Pages: 225-245

    • Peer Reviewed
  • [Presentation] Complex surface singularities with a fixed integral homology sphere link2017

    • Author(s)
      奥間智弘
    • Organizer
      日本数学会年会函数論分科会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-25 – 2017-03-25
  • [Presentation] Moderate degenerations of Calabi-Yau manifolds over higher dimensional bases2017

    • Author(s)
      高山 茂晴
    • Organizer
      Analytic Methods in Algebraic Geometry Day
    • Place of Presentation
      Northwestern Univ.,米国
    • Year and Date
      2017-03-18 – 2017-03-18
    • Int'l Joint Research / Invited
  • [Presentation] Some applications of the optimal L^2-extension theorem2017

    • Author(s)
      H. Tuji
    • Organizer
      Complex Geometry Seminar
    • Place of Presentation
      Universite de Paris VI, フランス
    • Year and Date
      2017-02-28 – 2017-02-28
    • Int'l Joint Research / Invited
  • [Presentation] Injectivity theorems with multiplier ideal sheaves for higher direct images2017

    • Author(s)
      松村 慎一
    • Organizer
      The 12th Algebraic-Analytic-Geometry seminar
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2017-02-14 – 2017-02-14
    • Invited
  • [Presentation] 多変量解析と多変数函数論の間で2016

    • Author(s)
      伊師英之
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      福井工業大学
    • Year and Date
      2016-12-17 – 2016-12-17
    • Invited
  • [Presentation] Scalar curvature as moment map in generalized Kahler geometry2016

    • Author(s)
      R. Goto
    • Organizer
      Generalized Geometry and Noncommutative Algebra
    • Place of Presentation
      Oxford 英国
    • Year and Date
      2016-12-08 – 2016-12-08
    • Int'l Joint Research / Invited
  • [Presentation] 局所ゼータ関数の漸近解析と有理型関数としての解析接続について2016

    • Author(s)
      野瀬 敏洋
    • Organizer
      複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2016-11-21 – 2016-11-21
    • Invited
  • [Presentation] Renormalized volume of strictly pseudoconvex domains2016

    • Author(s)
      K. Hirachi
    • Organizer
      Complex Analysis: Geometric and Dynamical Aspects
    • Place of Presentation
      Almora, インド
    • Year and Date
      2016-11-16 – 2016-11-16
    • Int'l Joint Research / Invited
  • [Presentation] Some remarks on special pseudo convex domains2016

    • Author(s)
      大沢健夫
    • Organizer
      Complex Analysis: Geometric and Dynamical Aspects
    • Place of Presentation
      Almora, インド
    • Year and Date
      2016-11-16 – 2016-11-16
    • Int'l Joint Research / Invited
  • [Presentation] A characterization of rational surface singularities via core of ideals2016

    • Author(s)
      T. Okuma
    • Organizer
      The 4th Franco-Japanese-Vietnamese Singularities
    • Place of Presentation
      University of Savoie Mont Blanc, フランス
    • Year and Date
      2016-11-08 – 2016-11-08
    • Int'l Joint Research / Invited
  • [Presentation] 管状領域のPaley-Wiener型定理と指数型分布族2016

    • Author(s)
      伊師 英之
    • Organizer
      複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2016-11-07 – 2016-11-07
    • Invited
  • [Presentation] 榎の単射性定理とその乗数イデアル層を用いて一般化2016

    • Author(s)
      松村 慎一
    • Organizer
      第22回複素幾何シンポジウム
    • Place of Presentation
      金沢県政記念 しいのき迎賓館
    • Year and Date
      2016-11-04 – 2016-11-04
    • Invited
  • [Presentation] Scalar curvature as moment map in generalized K\"ahler geometry2016

    • Author(s)
      R. Goto
    • Organizer
      第22回複素幾何シンポジウム
    • Place of Presentation
      金沢県政記念 しいのき迎賓館
    • Year and Date
      2016-11-04 – 2016-11-04
    • Invited
  • [Presentation] Pseudoconvexity and variation of Kahler-Einstein metrics2016

    • Author(s)
      辻元
    • Organizer
      第22回複素幾何シンポジウム
    • Place of Presentation
      金沢県政記念 しいのき迎賓館
    • Year and Date
      2016-11-03 – 2016-11-03
    • Invited
  • [Presentation] Positivity of the direct image of an adjoint bundle with multiplier ideal2016

    • Author(s)
      高山 茂晴
    • Organizer
      第22回複素幾何シンポジウム
    • Place of Presentation
      金沢県政記念 しいのき迎賓館
    • Year and Date
      2016-11-02 – 2016-11-02
    • Invited
  • [Presentation] On analytic continuation of local zeta functions2016

    • Author(s)
      J. Kamimoto
    • Organizer
      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 – 2016-10-07
    • Invited
  • [Presentation] 標準束の複素幾何学2016

    • Author(s)
      高山 茂晴
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-16 – 2016-09-16
    • Invited
  • [Presentation] 超越的な手法を用いた小平の消滅定理に一般化について2016

    • Author(s)
      松村 慎一
    • Organizer
      日本数学会 秋季総合分科会 函数論分科会 特別講
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-16 – 2016-09-16
    • Invited
  • [Presentation] Scalar curvature as moment map in generalized Kahler geometry2016

    • Author(s)
      R. Goto
    • Organizer
      The second China-Japan geometry conference
    • Place of Presentation
      Fujian Normal University, 中国
    • Year and Date
      2016-09-07 – 2016-09-07
    • Int'l Joint Research / Invited
  • [Presentation] Analytic methods in algebraic geometry2016

    • Author(s)
      松村 慎一
    • Organizer
      Intensive courses on Geometry and its Applications
    • Place of Presentation
      Pohang University of Science and Technology, 韓国
    • Year and Date
      2016-09-06 – 2016-09-11
    • Int'l Joint Research / Invited
  • [Presentation] Versions of injectivity and extension theorems2016

    • Author(s)
      松村 慎一
    • Organizer
      Seminar on Geometry and its Applications
    • Place of Presentation
      Pohang University of Science and Technology, 韓国
    • Year and Date
      2016-09-05 – 2016-09-05
    • Int'l Joint Research / Invited
  • [Presentation] Stratified flat structure on the moduli space of generalized complex surfaces2016

    • Author(s)
      R. Goto
    • Organizer
      HAYAMA Symposium on Complex Analysis in Several Variables XVIII
    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2016-07-17 – 2016-07-17
    • Int'l Joint Research / Invited
  • [Presentation] Injectivity theorem with multiplier ideal sheaves for higher direct images under K\"ahler morphisms2016

    • Author(s)
      松村 慎一
    • Organizer
      The KSCV Symposium 11: International conference on Complex Analysis and Geometry
    • Place of Presentation
      Kolon Hotel, Pohang, 韓国
    • Year and Date
      2016-07-05 – 2016-07-05
    • Int'l Joint Research / Invited
  • [Presentation] Algebraic Geometry of Twistor Spaces2016

    • Author(s)
      本多宣博
    • Organizer
      Conference on Differential Geometry
    • Place of Presentation
      CRM,Montreal, カナダ
    • Year and Date
      2016-07-05 – 2016-07-05
    • Int'l Joint Research / Invited
  • [Presentation] Total Q-prime curvature in view of scattering theory2016

    • Author(s)
      K. Hirachi
    • Organizer
      Pacific RIM Conference on Mathematics
    • Place of Presentation
      ソウル国立大学,韓国
    • Year and Date
      2016-07-01 – 2016-07-01
    • Int'l Joint Research / Invited
  • [Presentation] A transcendental approach to injectivity theorem for log canonical pairs2016

    • Author(s)
      松村 慎一
    • Organizer
      複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2016-06-20 – 2016-06-20
    • Invited
  • [Presentation] Holomorphic torsion invariants for K3 surfaces with involution and Borcherds products2016

    • Author(s)
      K.-I. Yoshikawa
    • Organizer
      Moduli spaces and modular forms
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach,Oberwolfach,ドイツ
    • Year and Date
      2016-04-26 – 2016-04-26
    • Int'l Joint Research / Invited
  • [Funded Workshop] HAYAMA Symposium on Complex Analysis in Several Variables XVIII2016

    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2016-07-16 – 2016-07-19

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Published: 2018-01-16  

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