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sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves

Synopsis

Usage:
sheafExt^n(F,G)
Scripted functor: sheafExt
Inputs:
- n, an integer
- F, a coherent sheaf
- G, a coherent sheaf
Outputs:
- a coherent sheaf, the n-th sheaf Ext of F and G

Description

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

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 Ext^n(module M, module N).

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

o1 = X

o1 : ProjectiveVariety

i2 : sheafExt^1(OO_X^1(2),OO_X(-11)^1)

o2 = 0

o2 : coherent sheaf on X

See also

OO -- the structure sheaf
sheafHom -- sheaf Hom
Hom -- module of homomorphisms
Ext -- compute an Ext module
HH -- general homology and cohomology functor
Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext