There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal form and Coxeter-Dynkin diagram (A_1, A_2, A_3, A_4, A_5, D_4, D_5, E_6 and E^~_6). The eight types of rational double points (the E^~_6 type being the one excluded) can occur in only 20 combinations on a cubic surface (of which Fischer 1986a gives 19): A_1, 2A_1, 3A_1, 4A_1, A_2, (A_2, A_1), 2A_2, (2A_2, A_1), 3A_2, A_3, (A_3, A_1), (A_3, 2A_1), A_4, (A_4, A_1), A_5, (A_5, A_1), D_4, D_5, and E_6 (Looijenga 1978, Bruce and Wall 1979, Fischer 1986a).
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