SheafOfRings -- the class of sheaves of rings

Description

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

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
variety(SheafOfRings) -- get the variety

For the programmer

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

SheafOfRings -- the class of sheaves of rings

Description

See also

Functions and methods returning a sheaf of rings :

Methods that use a sheaf of rings :

For the programmer