複素多様体上の作用素に付随した不変量の解析

复流形上与算子相关的不变量分析

• 批准号: 04452009
• 负责人: OHSAWA Takeo
• 金额: $ 3.97万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04452009/
• 关键词: L^2 cohomology; Bergman kernel; logarithmic Capacity; Teichmiiller space; analytic torsion; Bergman核; ベルグマン核; 擬凸領域; 〓方程式; 補間問題; 開リーマン面; ボイリング密度; ベルグマン計量; L^2estimate; Bergman計量; ∂^^--方程式

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).

L^2上同调群：对于具有奇异性的Kahler变种的L^2上同调群，所期望的Hodge理论的推广仍然是不完整的。然而，对于孤立奇点的情况，得到了一个完整的结果，并发表在Pure Math.22中的Advanced Study中。Bergman核：关于Bergman核的增长性质，得到了非常一般性质的全新结果。其中有对Suita猜想的部分答案(发表在名古屋数学杂志上)。吉川提出了一个有趣的计算具有圆锥奇点的Kahler簇的解析挠率(发表在J.Diff.G.‘95)。

项目成果

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

Takeo Osawa：“关于超凸域的 Beraman 核”Nagoya Math.J. 129. 43-52 (1993)

Takeo OHSAWA: "On the Bergman kernel of hyperconvex domains" Nagoya Math.J.129. 43-52 (1993)

Takeo OHSAWA：“论超凸域的伯格曼核”Nagoya Math.J.129。

大沢健夫: "On the extension of L^2 holomorphic functions IV:a new density concept." Geometry and Analysis on Complex Manifolds. 157-170 (1994)

Takeo Osawa：“L^2 全纯函数的扩展 IV：一个新的密度概念。” 157-170 (1994)

Takeo Ohsawa: "On the L^2 cohomology of isolated singularities" Advanced Stud.in Pure Math.22. 247-263 (1993)

Takeo Ohsawa：“论孤立奇点的 L^2 上同调”Advanced Stud.in Pure Math.22。

大沢健夫,K,Diederich: "An estimate for the Bergman distance on pseudoconvex domains" Ann.of Math.(1995)

Takeo Osawa, K, Diederich：“伪凸域上伯格曼距离的估计”Ann.of Math.(1995)