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

## Synopsis

• Usage:
Ican=canCurveWithFixedScroll(g,k,n)
• Inputs:
• g, an integer, the genus of the curve
• k, an integer, the degree of the line bundle on C
• n, an integer, the integer defining the characteristic p ($\ge n$) of the ground field
• Outputs:
• ICan, an ideal, the ideal of the canonical curve

## Description

This function computes the ideal of a g-nodal canonical curve with a degree k<g line bundle that 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 ] 1009 0 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 ]) 1009 0 7 1009 0 7 i6 : Iscroll = minors(2,Phi); ZZ o6 : Ideal of ----[t ..t ] 1009 0 7 i7 : Ican + Iscroll == Ican o7 = true