# relativeEquations -- compute the relative quadrics

## Synopsis

• Usage:
I = relativeEquations(a,b,k)
• Inputs:
• Outputs:
• I, an ideal, multi-graded ideal in the Cox ring

## Description

We compute the relative equations of a resonance degenerate K3 in case of k resonance. The first step consists in chooses a prime field which has a k-th root of unity. We then follow section 4 of the paper equations and syzygies of K3 carpets and unions of scrolls.

 i1 : I = relativeEquations(4,4,3) 2 2 o1 = ideal (s*v - v v , t*v - v v , u v - 14s*u v + 13u v , t*u v - 1 0 2 0 1 2 2 0 1 1 0 2 0 0 ------------------------------------------------------------------------ 2 2 2 14u v + 13u v , s*u - u u , t*u - u u , s*t*v v - v , s*t*u v - 2 1 1 2 1 0 2 0 1 2 0 1 2 1 0 ------------------------------------------------------------------------ 2 14s*t*u v + 13u v , s*t*u u - u ) 0 1 2 2 0 1 2 ZZ o1 : Ideal of --[s, t, u ..u , v ..v ] 61 0 2 0 2 i2 : betti I 0 1 o2 = total: 1 9 0: 1 . 1: . . 2: . 6 3: . 3 o2 : BettiTally