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SpaceCurves :: smoothDivisors

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 :

For the programmer

The object smoothDivisors is a method function.