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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 5, 12 1/3
NA2,0 x7+x3y2+x2y3+y5 18 5, 7 12/35
NA2,1 x7+x3y2+x2y3+y6 19 5, 7, 12 107/210
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
[Malg] x8+y8+z8+x2y2z2 215 8 25/4

Hertlings Conjecture

Sao Carlos, 08/02 http://www.singular.uni-kl.de