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K3Carpets :: relativeEquations

relativeEquations -- compute the relative quadrics

Synopsis

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

See also

Ways to use relativeEquations :

For the programmer

The object relativeEquations is a method function.