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

## Synopsis

• Scripted functor: sheafExt
• Usage:
sheafExt^n(F,G)
• Inputs:
• Outputs:
• , 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

## Ways to use this method:

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