CoherentSheaf -- the class of all coherent sheaves

Functions and methods returning a coherent sheaf :

• ambient(CoherentSheaf)
• CoherentSheaf ** CoherentSheaf -- tensor product 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 ~ -- 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
• tensor(CoherentSheaf,CoherentSheaf), see tensor -- tensor product

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(Module) -- gives the generators and relations of a module or a coherent sheaf.
• codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
• CoherentSheaf (*) -- sum of twists
• CoherentSheaf ^** ZZ -- tensor power
• degrees(CoherentSheaf) -- degrees of generators
• 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 -- 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
• CoherentSheaf LowerBound, see LowerBound -- the class of lower bound objects
• minimalPresentation(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)

For the programmer

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