sheafHom -- sheaf Hom

Usage:

sheafHom(F, G)
Inputs:
- F, a coherent sheaf or a sheaf of rings,
- G, a coherent sheaf or a sheaf of rings,
Optional inputs:
- DegreeLimit => ..., default value null
- MinimalGenerators => ..., default value true
- Strategy => ..., default value null
Outputs:
- a coherent sheaf, corresponding to homomorphisms from $M \to N$, where $F = \tilde M$ and $G = \tilde N$

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)))

Ways to use sheafHom:

sheafHom(CoherentSheaf,CoherentSheaf)
sheafHom(CoherentSheaf,SheafOfRings)
sheafHom(SheafOfRings,CoherentSheaf)
sheafHom(SheafOfRings,SheafOfRings)
sheafHom(CoherentSheaf,SheafMap) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
sheafHom(SheafMap,CoherentSheaf) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
sheafHom(SheafMap,SheafOfRings) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
sheafHom(SheafOfRings,SheafMap) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom

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.

sheafHom -- sheaf Hom

Description

Code

See also

Ways to use sheafHom:

For the programmer