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# conormal -- Computes the conormal variety

## Synopsis

• Usage:
conormal(I)
• Inputs:
• I, an ideal, in a polynomial ring $k[x_1,\dots, x_n]$ for a field $k$, defining a closed variety in $k^n$ (or in $\PP^n$ if the ideal is homogeneous).
• Outputs:
• C, an ideal defining the conormal variety in $k^n \times \PP^{n-1}$.

## Description

For a complex projective variety $X=V(I)\subset \PP^n$ this command computes the ideal of the conormal variety $Con(X)$ in $k^n \times \PP^{n-1}$.

 i1 : S=QQ[x..z] o1 = S o1 : PolynomialRing i2 : I=ideal(y^2*z-x^2) 2 2 o2 = ideal(y z - x ) o2 : Ideal of S i3 : conormal I 2 2 2 o3 = ideal (y*v - 2z*v , x*v + 2z*v , z*v - v , y*v - 2v v , y*z*v + 1 2 0 2 0 1 0 1 2 0 ------------------------------------------------------------------------ 2 2 2 x*v , y v + 2x*v , y z - x ) 1 0 2 o3 : Ideal of QQ[x..z, v ..v ] 0 2

## Ways to use conormal :

• conormal(Ideal)
• conormal(Ideal,Ring) (missing documentation)

## For the programmer

The object conormal is .