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

RelativeCanonicalResolution :: curveOnScroll

curveOnScroll -- Computes the ideal of a canonical curve on a normalized scroll in terms of generators of the scroll

Synopsis

Usage:
J=curveOnScroll(Ican,g,k)
Inputs:
- Ican, an ideal, ideal of a genus g canonical curve with a degree k line bundle on a normalized scroll
- g, an integer, the genus
- k, an integer, the degree of the line bundle on C
Outputs:
- Jcan, an ideal, ideal of the canonical curve in terms of generators of the scroll

Description

Given the ideal of a canonical curve on a normalized scroll, the function computes the ideal of the curve in terms of generators on the scroll.

i1 : (g,k,n) = (8,5,1000);

i2 : Ican = canCurveWithFixedScroll(g,k,n);

               ZZ
o2 : Ideal of ----[t , t , t , t , t , t , t , t ]
              1009  0   1   2   3   4   5   6   7

i3 : Jcan = curveOnScroll(Ican,g,k);

               ZZ
o3 : Ideal of ----[pp , pp , pp , pp , v, w]
              1009   0    1    2    3

i4 : betti Jcan

            0 1
o4 = total: 1 5
         0: 1 .
         1: . .
         2: . 4
         3: . 1

o4 : BettiTally

See also

canCurveWithFixedScroll -- Computes a g-nodal canonical curve with a degree k line bundle on a normalized scroll
resCurveOnScroll -- Computes the relative canonical resolution

Ways to use `curveOnScroll` :

curveOnScroll(Ideal,ZZ,ZZ)