SheafOfRings -- the class of sheaves of rings

i1 : X = Proj(QQ[x..z])

o1 = X

o1 : ProjectiveVariety

i2 : OO_X

o2 = OO
       X

o2 : SheafOfRings

i3 : OO_X^6

        6
o3 = OO
       X

o3 : coherent sheaf on X

Functions and methods returning a sheaf of rings :

• "Ring ~" -- see sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Variety,Ring) -- make a coherent sheaf of rings

Methods that use a sheaf of rings :

• "SheafOfRings (*)" -- see CoherentSheaf (*) -- sum of twists
• "SheafOfRings ^ ZZ" -- see CoherentSheaf ^ ZZ -- direct sum
• "SheafOfRings ZZ" -- see CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• "Ext^ZZ(CoherentSheaf,SheafOfRings)" -- see Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• "Ext^ZZ(SheafOfRings,CoherentSheaf)" -- see Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• "Ext^ZZ(SheafOfRings,SheafOfRings)" -- see Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• "Ext^ZZ(SheafOfRings,SumOfTwists)" -- see Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
• HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety
• "Hom(CoherentSheaf,SheafOfRings)" -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "Hom(SheafOfRings,CoherentSheaf)" -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "Hom(SheafOfRings,SheafOfRings)" -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "SheafOfRings LowerBound" -- see LowerBound -- the class of lower bound objects
• module(SheafOfRings) -- make or get a module
• "ring(SheafOfRings)" -- see ring -- get the associated ring of an object
• "sheafExt^ZZ(CoherentSheaf,SheafOfRings)" -- see sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves
• "sheafExt^ZZ(SheafOfRings,CoherentSheaf)" -- see sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves
• "sheafExt^ZZ(SheafOfRings,SheafOfRings)" -- see sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves
• "sheafHom(CoherentSheaf,SheafOfRings)" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• "sheafHom(SheafOfRings,CoherentSheaf)" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• "sheafHom(SheafOfRings,SheafOfRings)" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• SheafOfRings ^ List -- make a graded free coherent sheaf
• SheafOfRings Sequence (missing documentation)
• variety(SheafOfRings) -- get the variety

For the programmer

The object SheafOfRings is a type, with ancestor classes HashTable < Thing.