Toward the fundamental inequality for normal surface singularities

我们考虑了正则曲面奇点，得到了正则圈的自交数与几何亏格之间的一个不等式。我们的不等式是以纤维代数曲面的斜率不等式为模型的，因此比率应表示为基本亏格中的函数。利用规范分解，我们可以为循环型的双点和三点建立所需的不等式。在这种特殊情况下，它们为Durfee猜想提供了另一种证明。

We considered normal surface singularities in order to obtain an inequality between the self-intersection number of the canonical cycle and the geometric genus. Our inequality is modeled on the slope inequality for fibred algebraic surfaces, and thus the ratio shuld be expressed as a function in the fundamental genus. We could establish the desired inequalities for double and triple points of cyclic type, by using the canonical resolution. They lead us to another proof for Durfee's conjecture in such special cases.