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CoherentSheaf
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CoherentSheaf -- the class of all coherent sheaves
Functions and methods returning a coherent sheaf :
ambient(CoherentSheaf)
(missing documentation)
canonicalBundle
(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 ^ List
(missing documentation)
CoherentSheaf ^ ZZ
-- direct sum
SheafOfRings ^ ZZ
-- see
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)
image(SheafMap)
(missing documentation)
kernel(SheafMap)
(missing documentation)
minimalPresentation(CoherentSheaf)
(missing documentation)
prune(CoherentSheaf)
(missing documentation)
pullback(SheafMap,SheafMap)
(missing documentation)
pushout(SheafMap,SheafMap)
(missing documentation)
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)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(CoherentSheaf,SheafOfRings)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(SheafOfRings,CoherentSheaf)
-- see
sheafExt
-- sheaf Ext of coherent sheaves
sheafExt^ZZ(SheafOfRings,SheafOfRings)
-- see
sheafExt
-- sheaf Ext 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 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 ** SheafMap
(missing documentation)
CoherentSheaf == CoherentSheaf
(missing documentation)
CoherentSheaf == ZZ
(missing documentation)
CoherentSheaf ^ Array
(missing documentation)
CoherentSheaf _ Array
(missing documentation)
components(CoherentSheaf)
(missing documentation)
degrees(CoherentSheaf)
(missing documentation)
euler(CoherentSheaf)
-- Euler characteristic of coherent sheaf
eulers(CoherentSheaf)
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)
(missing documentation)
Ext^ZZ(CoherentSheaf,SumOfTwists)
-- global Ext
genera(CoherentSheaf)
genus(CoherentSheaf)
HH^ZZ(AffineVariety,CoherentSheaf)
(missing documentation)
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)
(missing documentation)
isWellDefined(CoherentSheaf)
(missing documentation)
CoherentSheaf LowerBound
-- see
LowerBound
-- the class of lower bound objects
map(CoherentSheaf,CoherentSheaf,Matrix)
(missing documentation)
map(CoherentSheaf,CoherentSheaf,Matrix,InfiniteNumber)
(missing documentation)
map(CoherentSheaf,CoherentSheaf,Matrix,ZZ)
(missing documentation)
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)
(missing documentation)
ring(CoherentSheaf)
-- the coordinate ring of the underlying variety
sheafHom(CoherentSheaf,SheafMap)
(missing documentation)
sheafHom(SheafMap,CoherentSheaf)
(missing documentation)
SheafMap ** CoherentSheaf
(missing documentation)
variety(CoherentSheaf)
-- get the variety
ZZ == CoherentSheaf
(missing documentation)
For the programmer
The object
CoherentSheaf
is
a
type
, with ancestor classes
HashTable
<
Thing
.