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sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom

Synopsis

Usage:
sheafHom(M,N)
Function: sheafHom
Inputs:
- M, a coherent sheaf
- N, a coherent sheaf
Outputs:
- a coherent sheaf, 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

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