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K3Carpets :: relativeResolution

relativeResolution -- compute the relative resolution

Synopsis

Description

We compute the relative resolution 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 : F = relativeResolution(5,4,3)

      ZZ                       1      ZZ                       9      ZZ                       16      ZZ                       9      ZZ                       1
o1 = (--[s, t, u ..u , v ..v ])  <-- (--[s, t, u ..u , v ..v ])  <-- (--[s, t, u ..u , v ..v ])   <-- (--[s, t, u ..u , v ..v ])  <-- (--[s, t, u ..u , v ..v ])
      61        0   2   0   2         61        0   2   0   2         61        0   2   0   2          61        0   2   0   2         61        0   2   0   2
                                                                                                                                       
     0                               1                               2                                3                               4

o1 : ChainComplex
i2 : betti F

            0 1  2 3 4
o2 = total: 1 9 16 9 1
         0: 1 .  . . .
         1: . 1  . . .
         2: . 7  8 1 .
         3: . 1  8 7 .
         4: . .  . 1 .
         5: . .  . . 1

o2 : BettiTally

See also

Ways to use relativeResolution :

For the programmer

The object relativeResolution is a method function.