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Macaulay2Doc :: cotangentSheaf(ProjectiveVariety)

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

Synopsis

Description

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, free
i4 : degree omega

o4 = 4

See also