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, free of rank 6

Functions and methods returning a sheaf of rings :

• minimalPresentation(SheafOfRings) (missing documentation)
• prune(SheafOfRings) (missing documentation)
• Ring ~ -- see sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Ring) -- make a coherent sheaf of rings
• sheaf(Variety) -- make a coherent sheaf
• 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
• HH^ZZ(Variety,SheafOfRings) (missing documentation)
• 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)
• ring(SheafOfRings) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• sheafExt^ZZ(CoherentSheaf,SheafOfRings) -- see sheafExt -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(SheafOfRings,CoherentSheaf) -- see sheafExt -- sheaf Ext of coherent sheaves
• sheafExt^ZZ(SheafOfRings,SheafOfRings) -- see sheafExt -- sheaf Ext of coherent sheaves
• sheafHom(CoherentSheaf,SheafOfRings) -- see sheafHom -- sheaf Hom
• sheafHom(SheafOfRings,CoherentSheaf) -- see sheafHom -- sheaf Hom
• sheafHom(SheafOfRings,SheafOfRings) -- see sheafHom -- sheaf Hom
• sheafHom(SheafMap,SheafOfRings) (missing documentation)
• sheafHom(SheafOfRings,SheafMap) (missing documentation)
• SheafMap ** SheafOfRings (missing documentation)
• SheafOfRings ** SheafMap (missing documentation)
• 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.