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1994 Fiscal Year Final Research Report Summary

複素多様体上の作用素に付随した不変量の解析

Research Project

Project/Area Number 04452009
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNagoya University

Principal Investigator

OHSAWA Takeo  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (30115802)

Co-Investigator(Kenkyū-buntansha) KOBAYASHI Ryoichi  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (20162034)
FUNAKI Tadahisa  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (60112174)
KITAOKA Yoshiyuki  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (40022686)
TSUCHIYA Akihiro  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (90022673)
AOMOTO Kazuhiko  Nagoya Univ.School of Sci.Prof., 理学部, 教授 (00011495)
Project Period (FY) 1992 – 1994
KeywordsL^2 cohomology / Bergman kernel / logarithmic Capacity / Teichmiiller space / analytic torsion
Research Abstract

L^2 cohomology groups : For the L^2 cohomology groups of Kahler varieties with singularities, the desired extension of the Hodge theory is still incomplete. However, for the isolated singularity case, a complete result was obtained and published in Advanced Stud.in Pure Math.22.
The Bergman kernel : With respect to the growth properties of the Bergman kernel, completely new results of quite general nature have been obtained. Among them are a partial answer to the Suita conjecture (to appear in Nagoya Math.J.). Yoshikawa came up with an interesting computation of the analytic torsion of Kahler varieties with conical singularities (to appear in J.Diff.G.'95).

  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] 大沢 健夫: "On the Beraman Kernel of hyperconvex domains" Nagoya Math.J. 129. 43-52 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大沢 健夫,Klas Diederich: "General cortinuity principles for the Bergman Kernel" International J.Math.5. 189-199 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大沢 健夫: "On the L^2 cohomology groups of isolated singularities" Advanced Studies in pure Math.22. 247-263 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大沢 健夫: "On the extension of L^2 holomorphicIV:A New Density concept." Geometry and Analysis on Complex Manitolds. 157-170 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 大沢 健夫,Klas Diederich: "An estimate for the Bergman distance on pseudoconvex domains" Ann.of Math.(1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉川 謙一: "On the residue of the spectral zeta functions of kahler manifolds with conical singularities" Journal of Differential Geometry. (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takeo Ohsawa: "On the L^2 cohomology of isolated singularities" Advanced Stud.in Pure Math.22. 247-263 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takeo OHSAWA: "On the Bergman kernel of hyperconvex domains" Nagoya Math.J.129. 43-52 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kenichi Yoshikawa: "On the residue of the spectral zeta functions of Kahler manifolds with conical singularities" to appear in J.Diff.G.(accepted for publication).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1996-04-15  

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