tangentSpace -- tangent space to a projective variety at a point

Synopsis

• Usage:

  tangentSpace(X,p)

  tangentSpace(p,X)

• Inputs:
  • X, an embedded projective variety
  • p, an embedded projective variety, a point on $X$
• Outputs:
  • an embedded projective variety, the embedded tangent space $T_p(X)$ to $X$ at the point $p$

Description

i1 : X = PP_(ZZ/333331)^(3,2);

o1 : ProjectiveVariety, threefold in PP^9

i2 : p := point X

o2 = point of coordinates [-63251, 140212, 25299, -105446, -91880, -117577, 129587, 38839, 41433, 1]

o2 : ProjectiveVariety, a point in PP^9

i3 : tangentSpace(X,p)

o3 = threefold in PP^9 cut out by 6 hypersurfaces of degree 1

o3 : ProjectiveVariety, threefold in PP^9

See also

• tangentCone(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)
• singularLocus(MultiprojectiveVariety) -- the singular locus of the variety
• dual(EmbeddedProjectiveVariety) -- the variety projectively dual to an embedded projective variety
• point(MultiprojectiveVariety) -- pick a random rational point on a multi-projective variety