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

Synopsis

• Function: tangentialChowForm

• Usage:

  tangentialChowForm(X,s)

• Inputs:
  • X, an embedded projective variety
  • s, an integer
• Optional inputs:
  • AffineChartGrass => ..., default value true,
  • AffineChartProj => ..., default value true,
  • AssumeOrdinary => ..., default value null,
  • Duality => ..., default value null,
  • SingularLocus => ..., default value null,
  • Variable => ..., default value null,
• Outputs:
  • an embedded projective variety, the subvariety of the appropriate Grassmannian defined by tangentialChowForm(ideal X,s)

Description

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

o1 : ProjectiveVariety, surface in PP^4

i2 : tangentialChowForm(X,1)

o2 = 5-dimensional subvariety of PP^9 cut out by 6 hypersurfaces of degrees 2^5 4^1 

o2 : ProjectiveVariety, 5-dimensional subvariety of PP^9 (subvariety of codimension 1 in GG(2,4) ⊂ PP^9)

i3 : ambientVariety oo

o3 = GG(2,4) ⊂ PP^9

o3 : ProjectiveVariety, GG(2,4)

See also

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