sheaf(Module) -- make a coherent sheaf

Synopsis

• Function: sheaf

• Usage:

  sheaf M

  M~

• Inputs:
  • M, a module, homogeneous
• Outputs:
  • a coherent sheaf, the coherent sheaf on a projective variety X corresponding to M

Description

i1 : R = QQ[x,y,z];

i2 : X = Proj R

o2 = X

o2 : ProjectiveVariety

i3 : M = R^{1,2,3}

      3
o3 = R

o3 : R-module, free, degrees {-1, -2, -3}

i4 : sheaf M

        1          1          1
o4 = OO  (1) ++ OO  (2) ++ OO  (3)
       X          X          X

o4 : coherent sheaf on X, free

i5 : M~

        1          1          1
o5 = OO  (1) ++ OO  (2) ++ OO  (3)
       X          X          X

o5 : coherent sheaf on X, free