Geometry of twistor spaces

扭量空间的几何

• 批准号: 15340022
• 负责人: FUJIKI Akira
• 金额: $ 6.02万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340022/
• 关键词: twistor space; self-dual metric; hyperkahler manifold; complex manifold; algebraic dimension; scalar curvature; surface of type VII; Inoue surface; 自己双対多様体; 群作用; Douady空間

1. We have shown the existence of anti-self-dual hermitian metrics on many of the complex surface of class VII. Having modified the method of Kim-Pontecorvo, which itself is the generalization of the method of Donaldson-Friedman, and applying this method to Joyce twistor spaces together with some special elementary divisors on them, we show that the resulting 3-dimensional complex space with normal crossings can be smoothed by deformations and among the resulting manifolds we get desired twistor space for surface of class VII. In order to identify the resulting surface we take a natural cycle of rational curves on the above elementary divisors and consider the smoothing of the resulting triples ; as a result we could show that the Inoue-Hirzebruch surface and parabolic Inoue surfaces (with real parameters).2. We have constructed a wide class of almost homomorphism compact non-Kahler complex manifolds under the special linear group G=SL(2,C). Given a natural equivariant compactification X of G and a geometrically finite Klein group Γ without cusps such a manifold is obtained as the quotient space by Γ of a maximal domain of discontinuity on X. From their construction they are intimately related with the 3-dimensional hyperbolic manifolds.

1.我们已经证明了存在的反自对偶埃尔米特度量的许多复杂的曲面类VII。通过对Kim-Pontecorvo方法的改进（它本身是Donaldson-Friedman方法的推广），并将此方法应用于Joyce扭量空间及其上的一些特殊的初等因子，我们证明了所得到的具有法向交叉的三维复空间可以通过形变光滑化，并且在所得流形中我们得到了VII类曲面所需的扭量空间.为了识别所得到的曲面，我们在上述基本因子上取一个有理曲线的自然循环，并考虑所得到的三元组的光滑性，结果我们可以证明Inoue-Hirzebruch曲面和抛物Inoue曲面（具有真实的参数）.在特殊线性群G=SL（2，C）下构造了一类几乎同态紧的非Kahler复流形.给定G的一个自然等变紧化X和一个无尖点的几何有限Klein群Γ，得到了这样一个流形作为X上极大不连续域的商空间。从它们的构造来看，它们与三维双曲流形密切相关。

项目成果

Mukai flops and derived categories

Mukai 失败和派生类别

• 发表时间: 2003
• 期刊: J.reine, Angew.Math. 560
• 作者: H.Ohta;K.Ono;R.Goto;T.Mabuchi;T.Mabuchi;A.Fujiki;R.goto;T.Mabuchi;T.Mabuchi;A.Fujiki;Ryushi Goto;Y.Namikawa
• 通讯作者: Y.Namikawa

Harmonic forms on compact symplectic 2-step nilmanifolds

紧辛2阶尼尔流形上的调和形式

• 发表时间: 2003
• 期刊: Coral Press Sci.Publ. 1
• 作者: Y.Sakane;T.Yamada
• 通讯作者: T.Yamada

T.Mabuchi: "Multiplier Hermitian Structures on Kahler manifolds"Nagoya Math.J.. 170. 1-43 (2003)

T.Mabuchi：“卡勒流形上的乘数埃尔米特结构”Nagoya Math.J.. 170. 1-43 (2003)

Y.Namikawa: "Mukai flops and derived categories"J.Reine Angew.Math.. 560. 65-76 (2003)

Y.Namikawa：“Mukai 失败和派生类别”J.Reine Angew.Math.. 560. 65-76 (2003)

Mukai flops an derived categories

向井翻牌衍生类别

• 发表时间: 2003
• 期刊: J.Reine Angew.Math. 560
• 作者: B.Fu;Y.Namikawa;Y.Namikawa;Y.Namikawa
• 通讯作者: Y.Namikawa