The singularity of the canonical model of compact Kähler manifolds
The singularity of the canonical model of compact Kähler manifolds
复制标题
紧凯勒流形规范模型的奇异性
DOI：
10.1007/bf01456340
复制
发表时间：
1988
影响因子：
1.4
通讯作者：
N. Nakayama
中科院分区：
文献类型：
--
作者：
N. Nakayama
定理设X是紧Kdhler流形，其正则环θ：= G H~ Cx（mKx））是双生成的.则在S：= Proj 9 t上存在有效的m> O ff~-因子A，使得（S，A）是对数终结的。显然，如果x（X）=-oo，0，1或dim X，这是正确的。实际上，正则奇点的概念是由Reid [IR]在流形X的研究中引入的，x（X）= dimX。这个定理首先由Kawamata I-Ka [3，（7.4）]证明。在[Ko，（3.16）]中，Kollfir证明了在上述定理的情形下，如果X是双纯的射影好极小模型，则S只有有理奇点。此外，如果K（X）= dimX-1，我们可以找到一个除数A，使得（S，A）是对数终结符，如IN 2，（0.4）]。
Theorem. Let X be a compact Kdhler manifold whose canonical ring 9~:= G H~ Cx (mKx)) is finitely generated. Then there exists an effective m> O ff~-divisor A on S:= Proj 9t such that (S, A) is log-terminal.Clearly this is true if x (X)=-oo, 0, 1 or dim X. In fact, the notion of canonical singularity was introduced by Reid IR] in the study of manifolds X with x (X)= dimX. This theorem is first conjectured by Kawamata I-Ka3,(7.4)]. In [Ko,(3.16)], Kollfir has proved that in the situation of the above theorem, S has only rational singularities, if X is bimeromorphic to a projective good minimal model. Furthermore if K (X)= dimX-1, we can find a divisor A such that (S, A) is logterminal as in IN2,(0.4)].