# computeBound -- compute the bound for the good types in case of k resonance

## Synopsis

• Usage:
(a,b) = computeBound(a1,b1,k)
c = computeBound k
• Inputs:
• Outputs:

## Description

The iterated mapping over the relative resolution of X_e(a,b) in the resonance scroll has betti numbers in a range of a general 2k-gonal canonical curve of genus a+b+1, if a,b are large enough, see ES2018. We compute the minimal type $(a,b) \equiv (a1,b1) \mod k$ where this becomes true.

In the second version c is the minimal value of a,b's for all congruence classes mod k. We conjecture that c=k^2-k.

 i1 : (a,b)=computeBound(6,4,3) o1 = (9, 7) o1 : Sequence i2 : computeBound 3 -- 0.190414 seconds elapsed -- 0.209272 seconds elapsed -- 0.212203 seconds elapsed -- 0.216192 seconds elapsed -- 0.219991 seconds elapsed -- 0.282482 seconds elapsed o2 = 6