论文标题
几何结构，Gromov秩序，Kodaira尺寸和简单量
Geometric structures, the Gromov order, Kodaira dimensions and simplicial volume
论文作者
论文摘要
我们引入了Kodaira维度的公理定义，并将Thurston几何形式分类为尺寸$ \ leq 5 $，以此Kodaira维度为单位。我们表明，Kodaira维度相对于由5个manifolds之间的非零程度的图定义的部分顺序是单调的。我们研究了我们定义与Kodaira维度传统概念的兼容性，尤其是Kodaira维度最高的尺寸。为此，我们建立了简单体积和霍明型kodaira维度之间的联系，这特别意味着任何平滑的Kähler3倍，具有非变化的简单体积具有顶部的Holomororphic Kodaira维度。
We introduce an axiomatic definition for the Kodaira dimension and classify Thurston geometries in dimensions $\leq 5$ in terms of this Kodaira dimension. We show that the Kodaira dimension is monotone with respect to the partial order defined by maps of non-zero degree between 5-manifolds. We study the compatibility of our definition with traditional notions of Kodaira dimension, especially the highest possible Kodaira dimension. To this end, we establish a connection between the simplicial volume and the holomorphic Kodaira dimension, which in particular implies that any smooth Kähler 3-fold with non-vanishing simplicial volume has top holomorphic Kodaira dimension.
