Study on Complex Manifolds

复流形研究

• 批准号: 06452001
• 负责人: NAKAMURA Iku
• 金额: $ 4.61万
• 依托单位: Hokkaido 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: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452001/
• 关键词: A cubic threefold; Compactifications of C^3; Foliation; Residue of a vector field; Open Whitney umbrella; Quasi-linear differential equation; Lagrange stable; Wed; 複素多様体; 3次超曲面; ファノ多様体

Nakamura has been studying compact complex manifolds which are homeomorpic to one of Fano manifolds. In the parper published 1996 January, he reported his consequence about 3 dimensional cubic hypersurfaces in P^4. He also proved similar results for complete intersections of two quadric hypersurfaces in P^5. There are some interesting examples of compactifiactions of C^3 among them.Tatsu Suwa studied residues of vector fields along singular subvarieties and proved some interesting formulas. Izumiya classified local multi-valued solutions of quasi-linear first order differential equations. Ishikawa proved that under some general conditions keeping the inner product invariant, any (Lagrange) stable and isotropic mapping is stably equivalent to a Whiltney umbrella.Nakai studied some families of codimension one foliations called webs. He completed a classification of associative 4-webs, whose study had been started by Poincare and others.

Nakamura一直在研究与范诺流形同构的紧复流形。在1996年1月发表的论文中，他报告了关于P^4中的三维立方超曲面的结论。他还证明了P^5中两个二次超曲面的完全相交的类似结果。其中有一些关于C^3紧化的有趣例子。Tatsu Suwa研究了向量场沿奇异子变种的残数，并证明了一些有趣的公式。Izumiya分类拟线性一阶微分方程的局部多值解。石川证明了在保持内积不变的一般条件下，任意（拉格朗日）稳定各向同性映射稳定等价于一个惠特尼伞。Nakai研究了一些称为网状的余维叶。他完成了联想四网的分类，这项研究是由庞加莱和其他人开始的。

项目成果

D.Lehmann and T.Suwa: "Residues of holomorphic vector fields relative to singular invariant subvarieties." J.of Diff.Geom.41. 165-192 (1995)

D.Lehmann 和 T.Suwa：“全纯向量场相对于奇异不变子类型的残差。”

T、Suwa: "Residusofholomorphic vector fields relative to sinyular invariant sobvarieties." J,of Diff,Geom. 41. 165-192 (1995)

T, Suwa：“与正弦不变 sobvarieties 相关的全纯向量场。”J，of Diff，Geom 41. 165-192 (1995)

G.Ishikawa: "Classification of generic integral diagrams and first order ordinary differential equations" Intermational J.of Math. 4. 447-489 (1994)

G.Ishikawa：“一般积分图和一阶常微分方程的分类”国际数学杂志。

G,Ishikawa: "Classification of generic integral diagrams and first order ordinary differential eguations." International J,of Math. 4. 447-489 (1994)

G，Ishikawa：“一般积分图和一阶常微分方程的分类。”

I,Nakai: "Nots on Versal Deformation of First Order PDES and Web Structure" J,Diff,Egvations. 118. 253-292 (1995)

I，Nakai：“关于一阶 PDES 和 Web 结构的 Versal 变形的注释”J，Diff，Egvations。