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

Synopsis

Function: cotangentSheaf
Usage:

cotangentSheaf X
Inputs:
- X, a projective variety
Optional inputs:
- Minimize => a Boolean value, default value true, whether to apply minimalPresentation to the result before returning it
Outputs:
- a coherent sheaf, the cotangent sheaf of the projective variety

This function computes the cotangent sheaf of the projective variety X.

As an example we verify Gauss-Bonnet's theorem on a plane quartic curve:

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

i4 : degree omega

o4 = 4