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

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

Synopsis

Description

Computes the ideal of a g-nodal canonical curve with a degree k<g line bundle, which lies on a normalized scroll. The construction of such curves is based on the Macaulay2 package kGonalNodalCurves

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 : genus Ican, degree Ican, dim Ican

o3 = (8, 14, 2)

o3 : Sequence
i4 : betti res(Ican, DegreeLimit => 1)

            0  1  2  3
o4 = total: 1 15 35 21
         0: 1  .  .  .
         1: . 15 35 21

o4 : BettiTally
i5 : Phi = matrix{{t_0,t_2,t_4,t_6},{t_1,t_3,t_5,t_7}}

o5 = | t_0 t_2 t_4 t_6 |
     | t_1 t_3 t_5 t_7 |

              ZZ                                  2        ZZ                                  4
o5 : Matrix (----[t , t , t , t , t , t , t , t ])  <--- (----[t , t , t , t , t , t , t , t ])
             1009  0   1   2   3   4   5   6   7          1009  0   1   2   3   4   5   6   7
i6 : Iscroll = minors(2,Phi);

               ZZ
o6 : Ideal of ----[t , t , t , t , t , t , t , t ]
              1009  0   1   2   3   4   5   6   7
i7 : Ican + Iscroll == Ican

o7 = true

See also

Ways to use canCurveWithFixedScroll :