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SpaceCurves :: cubicSurface

cubicSurface -- creates a cubicSurface

Description

This function takes a polynomial ring in 4 variables over a field as the coordinate ring of P3 and creates a CubicSurface in this ring. The equation of the cubic surface is computed from the blowup of 6 points in P2, listed in the key BlowUpPoints, along with a rational map P2 -> P3 whose base loci is the 6 given points.

Synopsis

  • Usage:
    X = quadricSurface(R)
  • Inputs:
  • Outputs: 
i1 : cubicSurface(ZZ/32003[x,y,z,w])

                            2           2        2         2                      2           2         2          2         3
o1 = ideal(2495x*y*z + 4036y z - 5934y*z  - 2495x w - 4289y w - 1194y*z*w + 10682z w - 8366x*w  + 214y*w  + 4197z*w  - 11134w )

o1 : CubicSurface

See also

Ways to use cubicSurface :

For the programmer

The object cubicSurface is a method function.