论文标题
奇异Kähler-Einstein电位的连续性
Continuity of singular Kähler-Einstein potentials
论文作者
论文摘要
在本说明中，我们研究了奇异空间上退化复合复合蒙格 - 安培方程（DCMAE）解决方案的一些规律性方面。首先，我们研究了在单数Stein空间上DCMAE的DIRICHLET问题，显示了一般的连续性结果。结果的结果是，在孤立的奇异点处，Kähler-Einstein电位是连续的。接下来，当参考类别属于真正的néron-severi群体时，我们建立了DCMAE解决方案的全球连续性。这尤其产生了Kähler-Einstein电位在任何不可还原的Calabi-yau品种上的连续性。
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Ampère equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity result. A consequence of our results is that Kähler-Einstein potentials are continuous at isolated singularities. Next, we establish the global continuity of solutions to DCMAE when the reference class belongs to the real Néron-Severi group. This yields in particular the continuity of Kähler-Einstein potentials on any irreducible Calabi-Yau variety.
