# smoothDivisors -- produces a list of smooth divisors of a given degree on a surface

## Description

Produces a List of Divisor of a given degree on a given surface. On the CubicSurface and the QuarticSurfaceRational the list is not exhaustive, but will include a divisor for each possible genus that a smooth curve can obtain.

## Synopsis

• Usage:
L = smoothDiviors(d,X)
• Inputs:
• Outputs:
• L, a list, of Divisors
 i1 : X = quadricSurface(ZZ/101[x,y,z,w]); i2 : L = smoothDivisors(5,X) o2 = {{1, 4}, {2, 3}} o2 : List

## Synopsis

• Usage:
L = smoothDiviors(d,X)
• Inputs:
• Outputs:
• L, a list, of Divisors
 i3 : X = cubicSurface(ZZ/101[x,y,z,w]); i4 : L = smoothDivisors(5,X) o4 = {{2, 1, 0, 0, 0, 0, 0}, {3, 1, 1, 1, 1, 0, 0}, {4, 2, 1, 1, 1, 1, 1}} o4 : List

## Synopsis

 i5 : X = quarticSurfaceRational(ZZ/101[x,y,z,w]); i6 : L = smoothDivisors(5,X) o6 = {{3, 0, 2, 1, 1, 1, 1, 1, 0, 0}, {3, 0, 1, 1, 1, 1, 1, 1, 1, 0}, {4, 1, ------------------------------------------------------------------------ 2, 1, 1, 1, 1, 1, 1, 1}} o6 : List

## Ways to use smoothDivisors :

• "smoothDivisors(ZZ,CubicSurface)"