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。我们已经显示了在VII类的许多复杂表面上存在反对二元的遗传学指标。修改了Kim-Pontecorvo的方法，这本身就是唐纳森·弗里德曼（Donaldson-Friedman）方法的概括，并将这种方法应用于乔伊斯（Joyce）扭转空间以及对它们的一些特殊基本鸿沟，我们表明，由此产生的三维复杂空间与正常交叉点可以通过不形式来平滑，在结果中，我们得到了所需的歧管，我们得到了所需的classor twistor classor twistor vistor vi vi vi vi vi vi vi。为了识别所得表面，我们在上述基本部门上进行自然的理性曲线循环，并考虑所得三元组的平滑。结果，我们可以证明inoue-hirzebruch表面和抛物线表面（带有实际参数）.2。我们已经在特殊的线性g = sl（2，c）下构建了一类宽类的几乎同态紧凑的非卡勒复合物。鉴于G的天然等效压实X的G和几何有限的klein klein组γ没有cusps，因此将这种歧管得出作为引用空间，作为γ的引文空间，即X上最大不连续性的最大域。从它们的结构中，它们与3维双皮折叠密切相关。

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)