论文标题
在平滑最小模型上存在CSCK指标
Existence of cscK metrics on smooth minimal models
论文作者
论文摘要
考虑到紧凑的Kähler歧管$ x $，有趣的是它是否承认恒定标态曲率Kähler（CSCK）度量。在此简短说明中，我们表明，与NEF规范捆绑包的紧凑型Kähler歧管上始终存在CSCK指标，因此在所有平滑的最小模型以及任何此类歧管的爆炸中也存在。这证实了对Jian-shi-song \ cite {jianshisong}的期望，并将其主要结果从$ k_x $ sem-sem-ample扩展到$ k_x $ nef，并直接证明对丰富的猜想没有吸引力。作为副产品，我们获得了紧凑的Kähler歧管的连接组件$ \ mathrm {aut} _0（x）$，$ k_x $ nef是微不足道的，要么是复杂的圆环。
Given a compact Kähler manifold $X$ it is interesting to ask whether it admits a constant scalar curvature Kähler (cscK) metric. In this short note we show that there always exist cscK metrics on compact Kähler manifolds with nef canonical bundle, thus on all smooth minimal models, and also on the blowup of any such manifold. This confirms an expectation of Jian-Shi-Song \cite{JianShiSong} and extends their main result from $K_X$ semi-ample to $K_X$ nef, with a direct proof that does not appeal to the Abundance conjecture. As a byproduct we obtain that the connected component $\mathrm{Aut}_0(X)$ of a compact Kähler manifold with $K_X$ nef is either trivial or a complex torus.
