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:
- a1, an integer,
- b1, an integer, type of the degenerate K3
- k, an integer, the resonance
Outputs:
- a, an integer,
- b, an integer, minimal good type
- c, an integer, lower bound for good a,b

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
 -- .101765s elapsed
 -- .0869936s elapsed
 -- .0921755s elapsed
 -- .113285s elapsed
 -- .101628s elapsed
 -- .122899s elapsed

o2 = 6

Ways to use computeBound:

computeBound(ZZ)
computeBound(ZZ,ZZ,ZZ)

For the programmer

The object computeBound is a method function.

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

Synopsis

Description

See also

Ways to use computeBound:

For the programmer