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sheafExt -- sheaf extension of coherent sheaves

Usage:

sheafExt^n(F,G)
Inputs:
- n, an integer,
- F, a sheaf of rings or a coherent sheaf,
- G, a sheaf of rings or a coherent sheaf,
Outputs:
- a coherent sheaf, the n-th sheaf extension 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.

Both F and S 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 F, module G).

i1 : X = Proj QQ[x,y]

o1 = X

o1 : ProjectiveVariety

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

o2 = 0

o2 : coherent sheaf on X, free of rank 0

See also

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

Ways to use sheafExt:

sheafExt^ZZ(CoherentSheaf,CoherentSheaf)
sheafExt^ZZ(CoherentSheaf,SheafOfRings)
sheafExt^ZZ(SheafOfRings,CoherentSheaf)
sheafExt^ZZ(SheafOfRings,SheafOfRings)

For the programmer

The object sheafExt is a scripted functor.

The source of this document is in Varieties/doc-functors.m2:600:0.