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Hertling's Conjecture for Newton non-Degenerate Singularities
| type |
f |
mu(f) |
denominators of SN |
g(f) |
| T3,4,5 |
z5+y4+xyz+x3 |
11 |
3, 4, 5 |
13/30 |
| T3,4,6 |
z6+y4+xyz+x3 |
12 |
4, 6 |
1/2 |
| T4,5,6 |
z6+y5+xyz+x4 |
14 |
4, 5, 6 |
23/30 |
| J3,1 |
x3+x2y3+y10 |
17 |
9, 20 |
1/10 |
| J3,2 |
x3+x2y3+y11 |
18 |
9, 11 |
20/99 |
| Z1,1 |
x3y+x2y3+y8 |
16 |
7, 16 |
1/8 |
| Z1,2 |
x3y+x2y3+y9 |
17 |
7, 9 |
16/63 |
| W1,1 |
x4+x2y3+y7 |
16 |
7, 12 |
1/7 |
| W1,2 |
x4+x2y3+y8 |
17 |
12, 16 |
7/24 |
| Q2,1 |
x3+yz2+x2y2+y7 |
15 |
12, 14 |
1/7 |
| Q2,2 |
x3+yz2+x2y2+y8 |
16 |
12, 16 |
7/24 |
| S1,1 |
x2z+yz2+x2y2+y6 |
15 |
10, 12 |
1/6 |
| S1,2 |
x2z+yz2+x2y2+y7 |
16 |
10, 14 |
12/35 |
| U1,1 |
x3+xz2+xy3+y2z2 |
15 |
9, 10 |
11/45 |
| 0 |
0 |
0 |
0 |
0 |
| NA1,0 |
x6+x3y2+x2y3+y5 |
17 |
5, 12 |
1/6 |
| NA1,1 |
x6+x3y2+x2y3+y6 |
18 |
0 |
0 |
| NA2,0 |
x7+x3y2+x2y3+y5 |
18 |
5, 7 |
12/35 |
| NA2,1 |
x7+x3y2+x2y3+y6 |
19 |
0 |
0 |
| 0 |
0 |
0 |
0 |
0 |
| NB(-1)0 |
x5+x3y2+y6 |
18 |
5, 18 |
4/45 |
| NB(-1)1 |
x6+x3y2+y6 |
19 |
12, 18 |
5/18 |
| NB(-1)2 |
x7+x3y2+y6 |
20 |
7, 18 |
10/21 |
| NB(-1)3 |
x8+x3y2+y6 |
21 |
16, 18 |
49/72 |
| NB(-1)4 |
x9+x3y2+y6 |
22 |
18 |
8/9 |
| 0 |
0 |
0 |
0 |
0 |
| NB(0)0 |
xy5+x3y2+x5 |
19 |
5, 13 |
8/65 |
| NB(0)1 |
xy5+x3y2+x6 |
20 |
12, 13 |
25/78 |
| NB(0)2 |
xy5+x3y2+x7 |
21 |
7, 13 |
48/91 |
| NB(0)3 |
xy5+x3y2+x8 |
22 |
13, 16 |
77/104 |
| NB(0)4 |
xy5+x3y2+x9 |
23 |
9, 13 |
112/117 |
| 0 |
0 |
0 |
0 |
0 |
| NB(1)0 |
y7+x3y2+x5 |
20 |
5, 21 |
16/105 |
| NB(1)1 |
y7+x3y2+x6 |
21 |
12, 21 |
5/14 |
| NB(1)2 |
y7+x3y2+x7 |
22 |
21 |
4/7 |
| NB(1)3 |
y7+x3y2+x8 |
23 |
16, 21 |
19/24 |
| NB(1)4 |
y7+x3y2+x9 |
24 |
9, 21 |
64/63 |
| 0 |
0 |
0 |
0 |
0 |
| 0 |
x6+x4y2+y7 |
28 |
6, 28 |
1/6 |
| 0 |
x7+x4y2+y7 |
29 |
28 |
4/7 |
| 0 |
x8+x4y2+y7 |
30 |
8, 28 |
27/28 |
| 0 |
x9+x4y2+y7 |
31 |
18, 28 |
85/63 |
| 0 |
x10+x4y2+y7 |
32 |
10, 28 |
121/70 |
| 0 |
0 |
0 |
0 |
0 |
| 0 |
x7+x5y2+y8 |
40 |
7, 40 |
1/7 |
| 0 |
x8+x5y2+y8 |
41 |
16,40 |
23/40 |
| 0 |
x9+x5y2+y8 |
42 |
9, 40 |
91/90 |
| 0 |
x10+x5y2+y8 |
43 |
40 |
29/20 |
| 0 |
x11+x5y2+y8 |
44 |
11,40 |
104/55 |
| 0 |
x12+x5y2+y8 |
45 |
24, 40 |
7/3 |
| 0 |
x13+x5y2+y8 |
46 |
13, 40 |
361/130 |
| 0 |
0 |
0 |
0 |
0 |
| [Altm] |
x5+y3z2+z5+y6 |
68 |
60 |
2/3 |
Hertlings Conjecture
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