# relativeResolutionTwists -- compute the twists in the relative resolution

## Synopsis

• Usage:
L = relativeResolutionTwists(am,bm,F)
• Inputs:
• Outputs:
• L, a list, of Lists of multidegrees

## Description

We compute the twists of the relative resolution in the resonance scroll of a degenerate K3 X_e(a,b) in case of k resonance after re-embedding the resonace scroll with |H+jR| for j=am-a_0=bm-b_0 where $\{a_i\}|\{b_j\}$ is the splitting type of the resonance scroll.

 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}| +--------------------+