论文标题
有限的小组动作在Symplectic Calabi-yau上$ 4 $ -Manifolds，$ b_1> 0 $
Finite group actions on symplectic Calabi-Yau $4$-manifolds with $b_1>0$
论文作者
论文摘要
这是一系列论文中的第一篇，专门针对Symplectic Calabi-yau $ 4 $ -MANIFOLDS，并具有某些符号有限的小组动作。我们完全确定在符号calabi-yau上有限循环作用的定点集结构，$ 4 $ -Manifold，$ b_1> 0 $。作为此固定点集分析的结果，$ 4 $ - manifold被证明是$ t^2 $ -Bundle $ t^2 $在某些情况下，例如，如果集体行动是一种限制，则可以在$ 4 $ -MANIFOLD中固定$ 2 $ -Dimensional的表面。我们关于Symplectic Calabi-yau $ 4 $ manifolds的项目基于对合理$ 4 $ manifold中某些配置的某些配置的不相交嵌入的存在和分类。本文为在同源层面上进行了这种分析奠定了基础。还获得了一些具有独立关注的结果，这些结果还获得了最大嵌入式嵌入式符号$（-2）$ - 在有理$ 4 $ -MANIFOLD中的球形。
This is the first of a series of papers devoted to the topology of symplectic Calabi-Yau $4$-manifolds endowed with certain symplectic finite group actions. We completely determine the fixed-point set structure of a finite cyclic action on a symplectic Calabi-Yau $4$-manifold with $b_1>0$. As an outcome of this fixed-point set analysis, the $4$-manifold is shown to be a $T^2$-bundle over $T^2$ in some circumstances, e.g., in the case where the group action is an involution which fixes a $2$-dimensional surface in the $4$-manifold. Our project on symplectic Calabi-Yau $4$-manifolds is based on an analysis of the existence and classification of disjoint embeddings of certain configurations of symplectic surfaces in a rational $4$-manifold. This paper lays the ground work for such an analysis at the homological level. Some other result which is of independent interest, concerning the maximal number of disjointly embedded symplectic $(-2)$-spheres in a rational $4$-manifold, is also obtained.
