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K3Carpets :: computeBound

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



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

See also

Ways to use computeBound :

For the programmer

The object computeBound is a method function.