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. 我们已经证明了在许多 VII 类复杂表面上存在反自对偶埃尔米特度量。修改了 Kim-Pontecorvo 的方法（该方法本身就是 Donaldson-Friedman 方法的推广），并应用了该方法。通过对乔伊斯扭曲空间的方法以及它们上的一些特殊的初等除数，我们证明了所得到的具有法向交叉的 3 维复空间可以通过变形进行平滑，并且在所得的流形中我们得到了所需的扭曲空间为了识别所得曲面，我们在上述基本除数上采用有理曲线的自然循环，并考虑所得三元组的平滑，结果我们可以证明 Inoue-Hirzebruch 曲面和抛物线 Inoue 曲面； （具有实数参数）.2.在给定自然等变紧化X的情况下，我们构造了一个宽类的几乎同态紧致非卡勒复流形。 G 和没有尖点的几何有限克莱因群 Γ 这样的流形是作为 X 上不连续的最大域的 Γ 的商空间获得的。从它们的构造来看，它们与 3 维双曲流形密切相关。

项目成果

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

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

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

B.Fu, Y.Namikawa: "Uniqueness of crepant resolutions and symplectic singularitie"Annales de l'Institut Fourier (Grenoble). (To appear).

B.Fu，Y.Namikawa：“Crepant 分辨率和辛奇点的唯一性”Annales de lInstitut Fourier（格勒诺布尔）。

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)