复射影平面上一个几何模型的构建

通过研究一个代数结果的几何图形表示,完成了复射影平面模型的构建,从而达到代数运算的准确结果和几何图形直观表示的完美统一．

复射影平面中全纯叶层的不变代数曲线和有理首次积分

借助代数几何作为工具给出复射影平面中一类全纯叶层具有有理首次积分的必要条件.进一步,得到复射影平面中一类全纯叶层的不可约不变代数曲线次数的上界.最后,应用所得结果证明了任何二次全纯叶层没有三次代数极限环.

四维流形与规范理论

在流形拓扑的理论中,我们研究的中心问题之一是对流形进行分类。基于换球术和h配边定理的几何技巧,在近30年内发展了高维流形的拓扑的详尽理论。在很大程度上对于高维流形弄清了这个问题。

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field,then any smooth connected fiber is also a K3 surface.Observing this,Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers.We shall give an explicit negative answer to his question in each dimension greater than or equal to three as well as a proof of his initial observation.