CoherentSheaf -- the class of all coherent sheaves

Functions and methods returning a coherent sheaf :

• ambient(CoherentSheaf) (missing documentation)
• CoherentSheaf ** CoherentSheaf -- tensor produce of coherent sheaves
• CoherentSheaf ++ CoherentSheaf -- direct sum of coherent sheaves
• CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
• "CoherentSheaf / Ideal" -- see CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
• CoherentSheaf ^ ZZ -- direct sum
• CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• "SheafOfRings ZZ" -- see CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety
• cotangentSheaf(ZZ,ProjectiveVariety) -- exterior powers of the cotangent sheaf of a projective variety
• "cover(CoherentSheaf)" -- see cover(Module) -- get the covering free module
• exteriorPower(ZZ,CoherentSheaf) -- exterior power
• "Module ~" -- see sheaf(Module) -- make a coherent sheaf
• sheaf(Module) -- make a coherent sheaf
• sheaf(Variety,Module) -- make a coherent sheaf
• sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves
• "sheafHom" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• "super(CoherentSheaf)" -- see super -- get the ambient module
• tangentSheaf(ProjectiveVariety) -- tangent sheaf of a projective variety

Methods that use a coherent sheaf :

• "Ideal * CoherentSheaf" -- see * -- a binary operator, usually used for multiplication
• "annihilator(CoherentSheaf)" -- see annihilator -- the annihilator ideal
• "betti(CoherentSheaf)" -- see betti -- display or modify a Betti diagram
• codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
• CoherentSheaf (*) -- sum of twists
• CoherentSheaf ^** ZZ -- tensor power
• "degrees(CoherentSheaf)" -- see degrees(Ring) -- degrees of generators
• "describe(CoherentSheaf)" -- see describe -- real description
• directSum(CoherentSheaf) (missing documentation)
• dual(CoherentSheaf) -- dual coherent sheaf
• euler(CoherentSheaf) -- Euler characteristic of coherent sheaf
• eulers(CoherentSheaf) -- list the sectional Euler characteristics
• Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• "Ext^ZZ(CoherentSheaf,SheafOfRings)" -- see Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• "Ext^ZZ(SheafOfRings,CoherentSheaf)" -- see Ext^ZZ(CoherentSheaf,CoherentSheaf) -- global Ext
• Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
• genera(CoherentSheaf) -- list of the successive linear sectional arithmetic genera
• genus(CoherentSheaf) -- arithmetic genus
• "HH^ZZ CoherentSheaf" -- see HH^ZZ(ProjectiveVariety,CoherentSheaf) -- cohomology of a coherent sheaf on a projective variety
• HH^ZZ(ProjectiveVariety,CoherentSheaf) -- cohomology of a coherent sheaf on a projective variety
• "hilbertFunction(List,CoherentSheaf)" -- see hilbertFunction -- the Hilbert function
• "hilbertFunction(ZZ,CoherentSheaf)" -- see hilbertFunction -- the Hilbert function
• hilbertPolynomial(CoherentSheaf) -- compute the Hilbert polynomial of the coherent sheaf
• Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "Hom(CoherentSheaf,SheafOfRings)" -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "Hom(SheafOfRings,CoherentSheaf)" -- see Hom(CoherentSheaf,CoherentSheaf) -- global Hom
• "CoherentSheaf LowerBound" -- see LowerBound -- the class of lower bound objects
• "minimalPresentation(CoherentSheaf)" -- see minimalPresentation(Module) -- minimal presentation of a module
• "prune(CoherentSheaf)" -- see minimalPresentation(Module) -- minimal presentation of a module
• module(CoherentSheaf) -- get the module defining a coherent sheaf
• numgens(CoherentSheaf) -- the number of generators of the underlying module
• pdim(CoherentSheaf) -- calculate the projective dimension
• "rank(CoherentSheaf)" -- see rank -- compute the rank
• "ring(CoherentSheaf)" -- 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
• sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• "sheafHom(CoherentSheaf,SheafOfRings)" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• "sheafHom(SheafOfRings,CoherentSheaf)" -- see sheafHom(CoherentSheaf,CoherentSheaf) -- sheaf Hom
• variety(CoherentSheaf) -- get the variety

For the programmer

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