Fano Manifolds with Weak almost Kähler–Ricci Solitons
Fano Manifolds with Weak almost Kähler–Ricci Solitons
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DOI：
10.1093/imrn/rnu006
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发表时间：
2013-07
影响因子：
1
通讯作者：
Xiaohua Zhu
中科院分区：
文献类型：
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作者：
Xiaohua Zhu
在Gromov-Hausdorff拓扑中，我们证明了一组弱几乎K\ ahler-Ricci孤子在进一步的适当条件下收敛于一个奇异度至少为2的复余维K\ ahler-Ricci孤子。作为一个推论，我们证明了在一个修正K能量有界的Fano流形上，存在一个弱几乎K\ ahler-Ricci孤子序列，这些孤子在Gromov-Hausdorff拓扑中收敛为具有至少2个奇异点的复余维数的K\ ahler-Ricci孤子。
In this paper, we prove that a sequence of weak almost K\"ahler-Ricci solitons under further suitable conditions converge to a K\"ahler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology. As a corollary, we show that on a Fano manifold with the modified K-energy bounded below, there exists a sequence of weak almost K\"ahler-Ricci solitons which converge to a K\"ahler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology.