cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety

Synopsis

• Function: cotangentSheaf

• Usage:

  cotangentSheaf X

• Inputs:
  • X, a projective variety
• Optional inputs:
  • MinimalGenerators => a Boolean value, default value true, whether to apply minimalPresentation to the result before returning it
  • Strategy (missing documentation) => ..., default value null,
• Outputs:
  • a coherent sheaf, the cotangent sheaf of the projective variety

Description

i1 : X=Proj(QQ[x,y,z]/(x^4+y^4+z^4))

o1 = X

o1 : ProjectiveVariety

i2 : genus(X)

o2 = 3

i3 : omega = cotangentSheaf(X)

        1
o3 = OO  (1)
       X

o3 : coherent sheaf on X, free of rank 1

i4 : degree omega

o4 = 4

See also

• tangentSheaf -- tangent sheaf of a projective variety
• ProjectiveVariety -- the class of all projective varieties