chowForm(EmbeddedProjectiveVariety) -- chow forms of a projective variety

Synopsis

• Function: chowForm

• Usage:

  chowForm X

• Inputs:
  • X, an embedded projective variety
• Optional inputs:
  • AffineChartGrass => ..., default value true,
  • AffineChartProj => ..., default value true,
  • Duality => ..., default value null,
  • Variable => ..., default value null,
• Outputs:
  • an embedded projective variety, the subvariety of the appropriate Grassmannian defined by chowForm ideal X

Description

i1 : X = PP_(ZZ/65521)[2,1];

o1 : ProjectiveVariety, surface in PP^4

i2 : chowForm X

o2 = 5-dimensional subvariety of PP^9 cut out by 6 hypersurfaces of degrees 2^5 3^1 

o2 : ProjectiveVariety, 5-dimensional subvariety of PP^9 (subvariety of codimension 1 in GG(1,4) ⊂ PP^9)

i3 : ambientVariety oo

o3 = GG(1,4) ⊂ PP^9

o3 : ProjectiveVariety, GG(1,4)

See also

• tangentialChowForm(EmbeddedProjectiveVariety,ZZ) -- higher Chow forms of a projective variety