# 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, the 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, the ideal of the canonical curve in terms of generators of the scroll

## Description

Given the ideal of a canonical curve on a normalized scroll, this 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 ] 1009 0 7 i3 : Jcan = curveOnScroll(Ican,g,k); ZZ o3 : Ideal of ----[pp ..pp , v..w] 1009 0 3 i4 : betti Jcan 0 1 o4 = total: 1 5 0: 1 . 1: . . 2: . 4 3: . 1 o4 : BettiTally