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

Synopsis

• Function: dual

• Usage:

  dual X

• Inputs:
  • X, an embedded projective variety
• Outputs:
  • an embedded projective variety, which is projectively dual to $X$

Description

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

o1 : ProjectiveVariety, surface in PP^5

i2 : X' = dual X;

o2 : ProjectiveVariety, hypersurface in PP^5

i3 : describe X'

o3 = ambient:.............. PP^5
     dim:.................. 4
     codim:................ 1
     degree:............... 3
     generators:........... 3^1 
     purity:............... true
     dim sing. l.:......... 2
     gens sing. l.:........ 2^6 

i4 : assert(dual X' == X)

See also

• conormalVariety(EmbeddedProjectiveVariety) -- the conormal variety of a projective variety
• dualVariety -- projective dual variety
• tangentSpace -- tangent space to a projective variety at a point