关于复格林函数的奇异性
On the singularities of the pluricomplex Green's function
摘要：
证明了在带边界的紧致卡勒流形上，具有多个极点的多元复格林函数的奇异性可以规定为每个极点处的形式为$\log\sum_{j=1}^n|f_j(z)|^2$，其中$f_j(z)$是以极点为唯一公共零点的任意局部全纯函数。证明是一个组合的爆破和最近的先验估计退化复杂的Monge-Ampere方程，特别是$C^1$估计远离一个除数。
英文摘要：
It is shown that, on a compact Kahler manifold with boundary, the singularities of the pluricomplex Green's function with multiple poles can be prescribed to be of the form $\log\sum_{j=1}^n|f_j(z)|^2$ at each pole, where $f_j(z)$ are arbitrary local holomorphic functions with the pole as their only common zero. The proof is a combination of blow-ups and recent a priori estimates for the degenerate complex Monge-Ampere equation, and particularly the $C^1$ estimates away from a divisor.
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