cotangentSheaf -- cotangent sheaf of a projective variety

Usage:

cotangentSheaf X
Inputs:
- X, a projective variety,
Optional inputs:
- MinimalGenerators => a Boolean value, default value true, whether to prune the result before returning it
- Strategy => ..., default value null
Outputs:
- a coherent sheaf,

Description

This method computes the cotangent sheaf of the projective variety $X$. The method used is to take the middle homology of the sequence associated to the Jacobian: --finish

As an example we verify the Gauss-Bonnet 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, free of rank 1

i4 : degree omega

o4 = 4

Ways to use cotangentSheaf:

cotangentSheaf(ProjectiveVariety)
cotangentSheaf(ZZ,ProjectiveVariety) -- exterior powers of the cotangent sheaf of a projective variety

For the programmer

The object cotangentSheaf is a method function with options.

The source of this document is in Varieties/doc-sheaves.m2:501:0.

cotangentSheaf -- cotangent sheaf of a projective variety

Description

See also

Ways to use cotangentSheaf:

For the programmer