Abstract
The Milnor number μ and the geometric genus pg of normal 2-dimensional double points are studied by using Zariski's canonical resolution. By using formulas due to E. HORIKAWA and H. LAUFER, we represent μ − 8pg in terms of the number of blowing-ups along ℙ1 and the number l of „even”︁ components in the resolution process. A key point of our arguments is the fact that if l is small then the resolution process is restricted very much. For rational double points and double points with pa = 1, each classes are characterized by numerical invariants appearing in this resolution process. For the case pa = 1, we can make our inequality sharper and can prove 12 · pg − 3 ≤ μ. This is an another proof of Xu-Yau's inequality for the singularity with pa = 1 in our situation.
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