SheafOfRings -- the class of sheaves of rings

Functions and methods returning a sheaf of rings:

• minimalPresentation(SheafOfRings) (missing documentation)
• OO _ Variety -- see OO -- the structure sheaf
• prune(SheafOfRings) (missing documentation)
• ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(SheafMap) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• ring(SheafOfRings) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• 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 -- canonical twist of a coherent sheaf
• expression(SheafOfRings) (missing documentation)
• 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
• isCommutative(SheafOfRings) (missing documentation)
• isLocallyFree(SheafOfRings) -- see isLocallyFree -- whether a coherent sheaf is locally free
• isWellDefined(SheafOfRings) (missing documentation)
• SheafOfRings LowerBound -- see LowerBound -- the class of lower bound objects
• mathML(SheafOfRings) (missing documentation)
• module(SheafOfRings)
• net(SheafOfRings) (missing documentation)
• sheafExt^ZZ(CoherentSheaf,SheafOfRings) -- see sheafExt -- sheaf extension of coherent sheaves
• sheafExt^ZZ(SheafOfRings,CoherentSheaf) -- see sheafExt -- sheaf extension of coherent sheaves
• sheafExt^ZZ(SheafOfRings,SheafOfRings) -- see sheafExt -- sheaf extension 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) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
• sheafHom(SheafOfRings,SheafMap) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
• SheafOfRings ^ List -- make a graded free coherent sheaf
• SheafOfRings ^ ZZ -- see SheafOfRings ^ List -- make a graded free coherent sheaf
• SheafOfRings Sequence (missing documentation)
• texMath(SheafOfRings) (missing documentation)
• toString(SheafOfRings) (missing documentation)
• variety(SheafOfRings) -- see variety(CoherentSheaf) -- the underlying variety over which a coherent sheaf or morphism is defined.

For the programmer

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

The source of this document is in Varieties/doc-sheaves.m2:62:0.