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# conormalVariety(EmbeddedProjectiveVariety) -- the conormal variety of a projective variety

- Function: conormalVariety
- Usage:
    `conormalVariety X`
- Inputs:
  - X, an embedded projective variety
- Optional inputs:
  - SingularLocus => ..., default value null,
  - Strategy => ..., default value "Saturate",
  - Variable => ..., default value null,
- Outputs:
  - a multi-projective variety, the conormal variety of $X$

## Description

    i1 : X = PP_QQ^(2,2);

    o1 : ProjectiveVariety, surface in PP^5

    i2 : C = conormalVariety X;

    o2 : ProjectiveVariety, 4-dimensional subvariety of PP^5 x PP^5

    i3 : p2 = multirationalMap last projections C;

    o3 : MultirationalMap (rational map from C to PP^5)

    i4 : image p2 == dual X

    o4 = true

## See also

- dual(EmbeddedProjectiveVariety) -- the variety projectively dual to an embedded projective variety

## Ways to use this method:

- conormalVariety(EmbeddedProjectiveVariety) -- the conormal variety of a projective variety

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:3952:0.