cotangentSheaf ProjectiveVariety -- cotangent sheaf of a variety

cotangentSheaf ProjectiveVariety -- cotangent sheaf of a variety

Synopsis:

Function: cotangentSheaf -- cotangent sheaf of a variety

Input:

an instance of class ProjectiveVariety.

Output:

an instance of class CoherentSheaf.

cotangentSheaf X -- calculate the cotangent sheaf of a variety X.

Code:

     -- ../../../Macaulay2/m2/varieties.m2:233-241
     cotangentSheaf ProjectiveVariety := CoherentSheaf => (X) -> (
          if X.cache.?cotangentSheaf
          then X.cache.cotangentSheaf
          else X.cache.cotangentSheaf = (
               R := ring X;
               F := presentation R;
               prune sheaf(X, homology(vars ring F ** R,jacobian F ** R))
               )
          )