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sheafHom -- sheaf Hom

Synopsis

Usage:

sheafHom(M,N)
Inputs:
- M
- N
Optional inputs:
- DegreeLimit (missing documentation) => ..., default value null,
- MinimalGenerators (missing documentation) => ..., default value true,
- Strategy (missing documentation) => ..., default value null,
Outputs:
- the coherent sheaf of homomorphisms from M to N

Description

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

M and N must be coherent sheaves on the same projective variety or scheme X.

The result is the sheaf associated to the graded module Hom(module M, module N).

i1 : X = Proj(QQ[x,y])

o1 = X

o1 : ProjectiveVariety

i2 : sheafHom(OO_X^1(2),OO_X(11)^1)

        1
o2 = OO  (9)
       X

o2 : coherent sheaf on X, free of rank 1

See also

OO -- the structure sheaf
sheafExt -- sheaf Ext of coherent sheaves
Hom -- module of homomorphisms
Ext -- compute an Ext module
HH -- general homology and cohomology functor
Hom(CoherentSheaf,CoherentSheaf) -- global Hom

Ways to use sheafHom:

sheafHom(CoherentSheaf,CoherentSheaf)
sheafHom(CoherentSheaf,SheafOfRings)
sheafHom(SheafOfRings,CoherentSheaf)
sheafHom(SheafOfRings,SheafOfRings)
sheafHom(CoherentSheaf,SheafMap) (missing documentation)
sheafHom(SheafMap,CoherentSheaf) (missing documentation)
sheafHom(SheafMap,SheafMap) (missing documentation)
sheafHom(SheafMap,SheafOfRings) (missing documentation)
sheafHom(SheafOfRings,SheafMap) (missing documentation)

For the programmer

The object sheafHom is a method function with options.