论文标题
最小紧凑的Kähler歧管的丰富定理与第二个Chern类消失
Abundance theorem for minimal compact Kähler manifolds with vanishing second Chern class
论文作者
论文摘要
在本文中，对于带有nef cotangent束的紧凑型kähler歧管，我们研究了丰度的猜想和相关的iitaka纤维。我们表明，对于最小的紧凑型kähler歧管，当且仅当cotangent捆绑包为nef且规范捆绑包的数值$ 0 $ 0 $或$ 1 $时，第二个Chern类就消失了。此外，在这种情况下，我们证明了规范捆绑包是半样本。此外，我们给出了IITAKA纤维纤维的变化与Cotangent束的一定半阳性之间的关系。
In this paper, for compact Kähler manifolds with nef cotangent bundle, we study the abundance conjecture and the associated Iitaka fibrations. We show that, for a minimal compact Kähler manifold, the second Chern class vanishes if and only if the cotangent bundle is nef and the canonical bundle has the numerical dimension $0$ or $1$. Additionally, in this case, we prove that the canonical bundle is semi-ample. Furthermore, we give a relation between the variation of the fibers of the Iitaka fibration and a certain semipositivity of the cotangent bundle.
