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cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety
Synopsis
Usage:
cotangentSheaf X
Function:
cotangentSheaf
Inputs:
X
,
a
projective variety
Outputs:
a
coherent sheaf
, the cotangent sheaf of the projective variety
Optional inputs
:
Minimize => ...
(missing documentation ),
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:
X=Proj(QQ[x,y,z]/(x^4+y^4+z^4))
genus(X)
omega = cotangentSheaf(X)
degree omega
See also
tangentSheaf
-- tangent sheaf of a projective variety
ProjectiveVariety
-- the class of all projective varieties