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SpaceCurves :: quarticSurfaceRational

quarticSurfaceRational -- creates a QuarticSurfaceRational

Description

This function takes a polynomial ring in 4 variables over a field as the coordinate ring of P3 and creates a rational quartic surface with a double line as a QuarticSurfaceRational in this ring. To do this We blow up P2 at 10 points, listed in BlowUpPoints, and map the blownup surface to P3. The map is specified as a rational map P2->P3 given in MapToP3.

Synopsis

i1 : X = quarticSurfaceRational(ZZ/32003[x,y,z,w])

            4        3          2 2          3        4        3         2             2         3         2 2            2        2 2           3         3       3          2             2         3          2                          2            2           2          2 2             2         2 2            2            2          3
o1 = ideal(x  + 9724x y - 14728x y  + 4857x*y  - 3225y  + 5278x z + 1636x y*z - 5528x*y z + 1012y z - 7898x z  + 2192x*y*z  + 8097y z  - 13288x*z  - 914y*z  - 813x w - 12824x y*w - 6277x*y w + 1492y w + 13647x z*w + 1491x*y*z*w + 12452y z*w - 914x*z w + 9994y*z w - 14516x w  + 10106x*y*w  + 14105y w  - 7003x*z*w  + 6180y*z*w  - 6180x*w )

o1 : QuarticSurfaceRational

See also

Ways to use quarticSurfaceRational :

For the programmer

The object quarticSurfaceRational is a method function.