next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
K3Carpets :: relativeResolution

relativeResolution

Synopsis

Description

We compute the relative resolution of a resonance degenerate K3 in case of k resonance. The first step consists in choosing a prime field which has a k-th root of unity. We then follow the proof of Theorem 4.12 (3) of [ES18].

i1 : F = relativeResolution(5,4,3)

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