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Macaulay2Doc :: sheafHom(CoherentSheaf,CoherentSheaf)

sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom

Synopsis

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)
-- ker (44) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (44) returned CacheFunction: -*a cache function*-
-- ker (44) called with Matrix: 0
--                                     1
-- ker (44) returned Module: (QQ[x..y])
assert( ker(map((QQ[x..y])^0,(QQ[x..y])^{{9}},0)) === ((QQ[x..y])^{{9}}))

        1
o2 = OO  (9)
       X

o2 : coherent sheaf on X, free

See also