论文标题
Kähler空间为零第一班级课程：Bochner原理，Albanese地图和基本组
Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups
论文作者
论文摘要
令$ x $成为一个紧凑的Kähler空间，具有KLT奇异性和消失的第一堂课。我们证明了在$ x $的光滑基因座上的全体形态张量的Bochner原理：相对于单数ricci-flat指标，任何此类张量都是平行的。因此，在有限的准泰尔覆盖$ x $之后，$ x $从最大可能的尺寸的复杂圆环中分解出来。然后，我们根据其自律代表来分解$ x $的切线捆。特别是，我们对具有强烈稳定的切线捆绑的$ x $进行分类：最多可覆盖，这些封面是不可约的calabi-yau-yau或不可还原的全态象征性的。作为这些结果的应用，我们表明，如果$ x $具有四个尺寸，那么它就可以满足Campana的Abelianity猜想。
Let $X$ be a compact Kähler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic tensors on the smooth locus of $X$: any such tensor is parallel with respect to the singular Ricci-flat metrics. As a consequence, after a finite quasi-étale cover $X$ splits off a complex torus of the maximum possible dimension. We then proceed to decompose the tangent sheaf of $X$ according to its holonomy representation. In particular, we classify those $X$ which have strongly stable tangent sheaf: up to quasi-étale covers, these are either irreducible Calabi--Yau or irreducible holomorphic symplectic. As an application of these results, we show that if $X$ has dimension four, then it satisfies Campana's Abelianity Conjecture.
