Macaulay2 » Documentation
Packages » K3Carpets :: relativeResolution
next | previous | forward | backward | up | index | toc

# relativeResolution -- compute the relative resolution

- Usage:
    `F = relativeResolution(a,b,k)`
- Inputs:
  - a, an integer,
  - b, an integer,
  - k, an integer,
- Outputs:
  - F, a complex, multi-graded chainComplex in the Cox ring

## 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 : Complex

    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

- relativeResolutionTwists -- compute the twists in the relative resolution
- relativeEquations -- compute the relative quadrics
- coxMatrices -- compute the Cox matrices

## Ways to use relativeResolution:

- `relativeResolution(ZZ,ZZ,ZZ)`

## For the programmer

The object relativeResolution is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/K3Carpets.m2:2020:0.