We compute the twists of the relative resolution in the resonance scroll of a degenerate K3 Xe(a,b) in case of k resonance after re-embedding the resonance scroll with |H+jR| for j=am-a0=bm-b0 where {ai }|{bj } is the splitting type of the resonance scroll, compare Theorem 4.12 and Remark 4.14 of [ES18].
i1 : F = relativeResolution(5,4,3); |
i2 : (as,bs)=resonanceScroll(5,4,3)
o2 = ({1, 1, 1}, {1, 1, 0})
o2 : Sequence
|
i3 : betti F
0 1 2 3 4
o3 = total: 1 9 16 9 1
0: 1 . . . .
1: . 1 . . .
2: . 7 8 1 .
3: . 1 8 7 .
4: . . . 1 .
5: . . . . 1
o3 : BettiTally
|
i4 : L = relativeResolutionTwists(as_0,bs_0,F); |
i5 : netList apply(L,c-> tally c)
+-------------------+
o5 = |Tally{{0, 0} => 1} |
+-------------------+
|Tally{{2, -1} => 7}|
| {2, -2} => 1 |
| {2, 0} => 1 |
+-------------------+
|Tally{{3, -1} => 8}|
| {3, -2} => 8 |
+-------------------+
|Tally{{4, -1} => 1}|
| {4, -2} => 7 |
| {4, -3} => 1 |
+-------------------+
|Tally{{6, -3} => 1}|
+-------------------+
|
i6 : L = relativeResolutionTwists(as_0+2,bs_0+1,F); |
i7 : netList apply(L,c-> tally c)
+--------------------+
o7 = |Tally{{0, 0} => 1} |
+--------------------+
|Tally{{2, -2} => 1} |
| {2, -3} => 2 |
| {2, -4} => 3 |
| {2, -5} => 2 |
| {2, -6} => 1 |
+--------------------+
|Tally{{3, -4} => 2} |
| {3, -5} => 4 |
| {3, -6} => 4 |
| {3, -7} => 4 |
| {3, -8} => 2 |
+--------------------+
|Tally{{4, -6} => 1 }|
| {4, -7} => 2 |
| {4, -8} => 3 |
| {4, -9} => 2 |
| {4, -10} => 1 |
+--------------------+
|Tally{{6, -12} => 1}|
+--------------------+
|