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WhitneyStratifications :: conormal

conormal -- Computes the conormal variety

Synopsis

Description

For a complex projective variety $X=V(I)\subset \PP^n$ this command computes the ideal of the conormal variety $Con(X)$ in $\PP^n \times (\PP^n)^*$.

i1 : S=QQ[x..z,w]

o1 = S

o1 : PolynomialRing
i2 : I=ideal(y^2*z-x^2*w)

            2     2
o2 = ideal(y z - x w)

o2 : Ideal of S
i3 : conormal I

                                                      2      2            
o3 = ideal (z*v  + w*v , y*v  + 2w*v , x*v  - 2w*v , v v  + v v , x*v v  -
               2      3     1       3     0       3   1 2    0 3     1 2  
     ------------------------------------------------------------------------
              2      2       2             2                 2      2     2  
     y*v v , x v  + y v , x*v  - 2z*v v , x v  + 2y*z*v , z*v  - w*v , y*v  -
        0 3     2      3     1       0 3     1         3     0      1     0  
     ------------------------------------------------------------------------
                                2               2     2
     2w*v v , y*z*v  + x*w*v , y v  + 2x*w*v , y z - x w)
         1 2       0        1     0         2

o3 : Ideal of QQ[x..z, w, v ..v ]
                           0   3

Ways to use conormal :

For the programmer

The object conormal is a method function.