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 |