多圈奇点、Lelong数和可积指数
Multi-circled singularities, Lelong numbers, and integrability index
摘要：
通过比较n维复空间中多圈多重次调和奇点的格林函数与其指标，得到了这类奇点的高Lelong数和可积指数的计算公式，并将Howald关于单项理想乘子理想的结果推广到多圈奇点.这也导致了一个初等的证明之间的关系的第k次Lelong数和可积指数。对于k=1和任意多重次调和函数，这个不等式是由Skoda提出的，而对于k=n和任意具有孤立奇点的多重次调和函数，这个关系是由Demailly提出的.我们还描述了多圈函数的不等式是平等的。通过对Demailly不等式的一个简化，我们也证明了这些不等式在多重次调和函数的一般情况下的存在性.此外，我们还得到了所有可积指数由Skoda不等式的下界给出的多重次调和奇点的描述。
英文摘要：
By comparing Green functions of multi-circled plurisubharmonic singularities in the n-domensional complex space to their indicators, we obtain formulas for the higher Lelong numbers and integrability index for such singularities and extend Howald's result on multiplier ideals for monomial ideals to multi-circled singularities. This also leads to an elementary proof of the relations between the k-th Lelong numbers and the integrability index. For k=1 and arbitrary plurisubharmonic functions the inequality is due to Skoda, and for k=n and any plurisubharmonic function with isolated singularity the relation is due to Demailly. We also describe multi-circled functions for which the inequalities are equalities. By a reduction to Demailly's inequality we prove these inequalities in the general case of plurisubharmonic functions as well. In addition, we get a description of all plurisubharmonic singularities whose integrability index is given by the lower bound in Skoda's inequality.
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