Twistor spaces over the connected sum of 3 projective planes
Twistor spaces over the connected sum of 3 projective planes
复制标题
3 个射影平面的连接和上的扭曲空间
作者：
B. Kreußler;H. Kurke
.在单连通紧扭量空间Z上的半反正则线性系统定义的映射中，假设Z的扭量线空间X上的自然自对偶共形结构包含一个具有正数量曲率的度量，且X的特征标度为3.利用M.弗里德曼，X必须同胚于3个复射影平面的连通和。最近，S.K.唐纳森和R.弗里德曼在更一般的背景下证明了这种扭量空间的存在。我们的结果导致所有复杂的紧凑的3倍，可以出现这样的扭量空间的分类。
. We consider the map defined by the half-anticanonical linear system on a simply connected compact twistor space Z under the hypothesis that the natural self-dual conformal structure on the space X of twistor lines of Z contains a metric with positive scalar curvature and that X has signature 3. By well-known results of M. Freedman, X has to be homeomorphic to a connected sum of 3 complex projective planes. Recently, S.K. Donaldson and R. Friedman showed the existence of such twistor spaces in a more general context. Our result leads to a classification of all complex compact 3-folds that can arise as such twistor spaces.