论文标题
几乎复杂歧管的Kodaira尺寸II
Kodaira dimensions of almost complex manifolds II
论文作者
论文摘要
这是一系列论文中的第二个，我们研究了plurigenera，Kodaira维度和Iitaka维度，紧凑几乎是复杂的歧管。通过使用伪酚类多态性多形绘图，我们在紧凑的几乎复杂的歧管上定义了Kodaira维度的第二版以及Iitaka尺寸。我们显示了具有顶部Kodaira维度的几乎复杂的结构是可以集成的。对于带有Kodaira尺寸的紧凑型几乎复杂的4个manifolds，我们获得了椭圆形纤维化，例如结构描述。在复杂的几何形状中，一些消失的定理被推广到几乎复杂的环境。 对于驯服的符合性$ 4 $ - manifolds，我们表明，几乎是kodaira维度在上面由象征性的kodaira维度界定，并使用概率的组合式风格参数。附录还包含一些结果，包括回答第二作者的问题，即非理性符号符合性$ 4 $ manifolds中有独特的子各种，以及通过对某些简化的同源球的符号嵌入来扩大对某些简化的同源球的限制，通过对截面形式进行假设。
This is the second of a series of papers where we study the plurigenera, the Kodaira dimension and the Iitaka dimension on compact almost complex manifolds. By using the pseudoholomorphic pluricanonical map, we define the second version of Kodaira dimension as well as Iitaka dimension on compact almost complex manifolds. We show the almost complex structures with the top Kodaira dimension are integrable. For compact almost complex 4-manifolds with Kodaira dimension one, we obtain elliptic fibration like structural description. Some vanishing theorems in complex geometry are generalized to the almost complex setting. For tamed symplectic $4$-manifolds, we show that the almost Kodaira dimension is bounded above by the symplectic Kodaira dimension, by using a probabilistic combinatorics style argument. The appendix also contains a few results including answering a question of the second author that there is a unique subvariety in exceptional curve classes for irrational symplectic $4$-manifolds, as well as extending Evans-Smith's constraint on symplectic embeddings of certain rational homology balls by removing the assumption on the intersection form.
