论文标题
Chern类别的偏光流和NEF矢量束的不平等现象
Chern class inequalities on polarized manifolds and nef vector bundles
论文作者
论文摘要
本文涉及Chern类和Chern数量的不平等现象和NEF矢量束。对于一对两对$（m，l）的$，$ l $非常丰富，我们的第一个主要结果是一个尖锐的Chern类不平等的家庭。其中第一个是经典结果的变体，第二个结果的平等案例是超出表面的表征。第二个主要结果是其上的Chern数字不平等，其中包括反向Miyaoka-yau类型的不等式。第三个主要结果是，紧凑型kähler歧管上的nef矢量束的Chern数在下面由Euler编号界定。作为一种应用，我们将紧凑型kähler歧管分类为非负性弯曲曲率，其Chern数字都是阳性的。提出了与带有非阳性双向曲率的紧凑型kähler歧管数量有关的猜想，这可以看作是与Hopf猜想的复杂类似物。
This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities. Among them the first one is a variant of a classical result and the equality case of the second one is a characterization of hypersurfaces. The second main result is a Chern number inequality on it, which includes a reverse Miyaoka-Yau type inequality. The third main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.
