CoherentSheaf -- the class of all coherent sheaves

Functions and methods returning a coherent sheaf:

• ambient(CoherentSheaf) (missing documentation)
• canonicalBundle -- the canonical bundle of a projective variety
• 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 ^ List -- see CoherentSheaf ^ ZZ -- direct sum
• CoherentSheaf ^ ZZ -- direct sum
• CoherentSheaf ^** ZZ -- tensor power
• CoherentSheaf Sequence (missing documentation)
• CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• SheafOfRings ZZ -- see CoherentSheaf ZZ -- canonical twist of a coherent sheaf
• coimage(SheafMap) (missing documentation)
• cokernel(SheafMap) (missing documentation)
• cotangentSheaf -- cotangent sheaf of a projective variety
• cover(CoherentSheaf) (missing documentation)
• determinant(CoherentSheaf) (missing documentation)
• directSum(CoherentSheaf) (missing documentation)
• dual(CoherentSheaf) -- dual coherent sheaf
• exteriorPower(ZZ,CoherentSheaf)
• homology(SheafMap,SheafMap) (missing documentation)
• Ideal * CoherentSheaf (missing documentation)
• idealSheaf -- ideal sheaf of a projective variety
• image(SheafMap) (missing documentation)
• kernel(SheafMap) (missing documentation)
• minimalPresentation(CoherentSheaf) -- minimal presentation of a coherent sheaf or sheaf map
• prune(CoherentSheaf) -- see minimalPresentation(CoherentSheaf) -- minimal presentation of a coherent sheaf or sheaf map
• pullback(SheafMap,SheafMap) (missing documentation)
• pushout(SheafMap,SheafMap) (missing documentation)
• Ideal ^~ -- see sheaf(Module) -- make a coherent sheaf
• Module ^~ -- see sheaf(Module) -- make a coherent sheaf
• sheaf(Ideal) -- see sheaf(Module) -- make a coherent sheaf
• sheaf(Module) -- make a coherent sheaf
• sheaf(Variety,Ideal) -- see sheaf(Variety,Module) -- make a coherent sheaf
• sheaf(Variety,Module) -- make a coherent sheaf
• sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- see sheafExt -- sheaf extension of coherent sheaves
• 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 -- sheaf Hom
• sheafHom(CoherentSheaf,CoherentSheaf) -- see sheafHom -- sheaf Hom
• sheafHom(CoherentSheaf,SheafOfRings) -- see sheafHom -- sheaf Hom
• sheafHom(SheafOfRings,CoherentSheaf) -- see sheafHom -- sheaf Hom
• sheafHom(SheafOfRings,SheafOfRings) -- see sheafHom -- 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)
• source(SheafMap) (missing documentation)
• super(CoherentSheaf) (missing documentation)
• symmetricPower(ZZ,CoherentSheaf) (missing documentation)
• tangentSheaf -- tangent sheaf of a projective variety
• target(SheafMap) (missing documentation)
• tensor(CoherentSheaf,CoherentSheaf) (missing documentation)

Methods that use a coherent sheaf:

• annihilator(CoherentSheaf) -- the annihilator ideal
• betti(CoherentSheaf) (missing documentation)
• codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
• CoherentSheaf (*) -- sum of twists
• CoherentSheaf == Module (missing documentation)
• components(CoherentSheaf) (missing documentation)
• degrees(CoherentSheaf) -- degrees of a coherent sheaf
• euler(CoherentSheaf) -- Euler characteristic of coherent sheaf
• eulers(CoherentSheaf)
• expression(CoherentSheaf) (missing documentation)
• 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,SheafMap) -- maps on global Ext induced by a sheaf map
• Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
• genera(CoherentSheaf)
• genus(CoherentSheaf)
• HH^ZZ(AffineVariety,CoherentSheaf)
• 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
• 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
• inducedMap(CoherentSheaf,CoherentSheaf) -- induced maps on coherent sheaves
• inducedMap(CoherentSheaf,CoherentSheaf,SheafMap) -- see inducedMap(CoherentSheaf,CoherentSheaf) -- induced maps on coherent sheaves
• isIsomorphic(CoherentSheaf,CoherentSheaf) (missing documentation)
• isLocallyFree(CoherentSheaf) -- see isLocallyFree -- whether a coherent sheaf is locally free
• isomorphism(CoherentSheaf,CoherentSheaf) (missing documentation)
• isWellDefined(CoherentSheaf) -- whether a coherent sheaf is well-defined
• CoherentSheaf LowerBound -- see LowerBound -- the class of lower bound objects
• map(CoherentSheaf,CoherentSheaf,Matrix) -- the constructor of morphisms of coherent sheaves
• map(CoherentSheaf,CoherentSheaf,Matrix,InfiniteNumber) -- see map(CoherentSheaf,CoherentSheaf,Matrix) -- the constructor of morphisms of coherent sheaves
• map(CoherentSheaf,CoherentSheaf,Matrix,ZZ) -- see map(CoherentSheaf,CoherentSheaf,Matrix) -- the constructor of morphisms of coherent sheaves
• map(CoherentSheaf,Nothing,Matrix) -- see map(CoherentSheaf,CoherentSheaf,Matrix) -- the constructor of morphisms of coherent sheaves
• map(Nothing,CoherentSheaf,Matrix) -- see map(CoherentSheaf,CoherentSheaf,Matrix) -- the constructor of morphisms of coherent sheaves
• map(CoherentSheaf,CoherentSheaf,SheafMap) (missing documentation)
• map(CoherentSheaf,CoherentSheaf,ZZ) (missing documentation)
• map(CoherentSheaf,Module,ZZ) (missing documentation)
• map(Module,CoherentSheaf,ZZ) (missing documentation)
• mathML(CoherentSheaf) (missing documentation)
• Module == CoherentSheaf (missing documentation)
• module(CoherentSheaf) -- get the module defining a coherent sheaf
• net(CoherentSheaf) (missing documentation)
• numgens(CoherentSheaf) -- the number of generators of the underlying module
• pdim(CoherentSheaf) -- calculate the projective dimension
• random(CoherentSheaf,CoherentSheaf) -- generate a random map of coherent sheaves
• rank(CoherentSheaf) -- rank of a coherent sheaf
• ring(CoherentSheaf) -- the coordinate ring of the underlying variety
• sheafHom(CoherentSheaf,SheafMap) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
• sheafHom(SheafMap,CoherentSheaf) -- see sheafHom(SheafMap,SheafMap) -- functor of sheaf Hom
• texMath(CoherentSheaf) (missing documentation)
• toString(CoherentSheaf) (missing documentation)
• variety(CoherentSheaf) -- the underlying variety over which a coherent sheaf or morphism is defined.

For the programmer

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

The source of this document is in Varieties/doc-sheaves.m2:64:0.