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sheafHom -- sheaf Hom

Description

If F or G is a sheaf of rings, it is regarded as a sheaf of modules in the evident way.

Both F and G must be coherent sheaves on the same projective variety or scheme $X$.

The result is the sheaf associated to the graded module Hom(module F, module G).

i1 : S = QQ[x,y]

o1 = S

o1 : PolynomialRing
i2 : X = Proj S

o2 = X

o2 : ProjectiveVariety
i3 : sheafHom(OO_X^1(2), OO_X^1(11))

        1
o3 = OO  (9)
       X

o3 : coherent sheaf on X, free of rank 1
i4 : Hom(S^{2}, S^{11})

      1
o4 = S

o4 : S-module, free, degrees {-9}

Code

../../../../Macaulay2/packages/Varieties.m2:711:59-712:77: --source code:
sheafHom(CoherentSheaf, CoherentSheaf) := CoherentSheaf => opts -> (F, G) -> (
    assertSameVariety(F, G); sheaf(variety F, Hom(module F, module G, opts)))

See also

Ways to use sheafHom:

For the programmer

The object sheafHom is a method function with options.


The source of this document is in Varieties/doc-functors.m2:600:0.