Macaulay2
»
Documentation
Packages
»
NormalToricVarieties
::
Table of Contents
next  previous  forward  backward  up 
index

toc
NormalToricVarieties : Table of Contents
NormalToricVarieties
 working with normal toric varieties and related objects
abstractSheaf(NormalToricVariety,AbstractVariety,CoherentSheaf)
 make the corresponding abstract sheaf
abstractSheaf(NormalToricVariety,AbstractVariety,ToricDivisor)
 make the corresponding abstract sheaf
abstractVariety(NormalToricVariety,AbstractVariety)
 make the corresponding abstract variety
affineSpace(ZZ)
 make an affine space as a normal toric variety
cartesianProduct(Sequence)
 make the Cartesian product of normal toric varieties
cartierDivisorGroup(NormalToricVariety)
 compute the group of torusinvariant Cartier divisors
cartierDivisorGroup(ToricMap)
 make the induced map between groups of Cartier divisors.
ch(ZZ,CoherentSheaf)
 compute the Chern character of a coherent sheaf
chern(ZZ,CoherentSheaf)
 compute the Chern class of a coherent sheaf
chi(CoherentSheaf)
 compute the Euler characteristic of a coherent sheaf
Chow ring
 make the rational Chow ring
classGroup(NormalToricVariety)
 make the class group
classGroup(ToricMap)
 make the induced map between class groups
components(NormalToricVariety)
 list the factors in a product
cotangentSheaf(NormalToricVariety)
 make the sheaf of Zariski 1forms
ctop(CoherentSheaf)
 compute the top Chern class of a coherent sheaf
degree(ToricDivisor)
 make the degree of the associated rankone reflexive sheaf
diagonalToricMap
 make a diagonal map into a Cartesian product
dim(NormalToricVariety)
 get the dimension of a normal toric variety
divisor arithmetic
 perform arithmetic on toric divisors
entries(ToricDivisor)
 get the list of coefficients
expression(NormalToricVariety)
 get the expression used to format for printing
expression(ToricDivisor)
 get the expression used to format for printing
fan(NormalToricVariety)
 make the 'Polyhedra' fan associated to the normal toric variety
finding attributes and properties
 information about accessing features of a normal toric variety
fromCDivToPic(NormalToricVariety)
 get the map from Cartier divisors to the Picard group
fromCDivToWDiv(NormalToricVariety)
 get the map from Cartier divisors to Weil divisors
fromPicToCl(NormalToricVariety)
 get the map from Picard group to class group
fromWDivToCl(NormalToricVariety)
 get the map from the group of Weil divisors to the class group
HH^ZZ(NormalToricVariety,CoherentSheaf)
 compute the cohomology of a coherent sheaf
hilbertPolynomial(NormalToricVariety)
 compute the multivariate Hilbert polynomial
hilbertPolynomial(NormalToricVariety,CoherentSheaf)
 compute the multivariate Hilbert polynomial
hirzebruchSurface(ZZ)
 make any Hirzebruch surface
id _ NormalToricVariety
 make the identity map from a NormalToricVariety to itself
ideal(NormalToricVariety)
 make the irrelevant ideal
ideal(ToricMap)
 make the ideal defining the closure of the image
inducedMap(ToricMap)
 make the induced map between total coordinate rings (a.k.a. Cox rings)
isAmple(ToricDivisor)
 whether a torusinvariant Weil divisor is ample
isCartier(ToricDivisor)
 whether a torusinvariant Weil divisor is Cartier
isComplete(NormalToricVariety)
 whether a toric variety is complete
isDegenerate(NormalToricVariety)
 whether a toric variety is degenerate
isDominant(ToricMap)
 whether a toric map is dominant
isEffective(ToricDivisor)
 whether a torusinvariant Weil divisor is effective
isFano(NormalToricVariety)
 whether a normal toric variety is Fano
isFibration(ToricMap)
 whether a toric map is a fibration
isNef(ToricDivisor)
 whether a torusinvariant Weil divisor is nef
isProjective(NormalToricVariety)
 whether a toric variety is projective
isProper(ToricMap)
 whether a toric map is proper
isQQCartier(ToricDivisor)
 whether a torusinvariant Weil divisor is QQCartier
isSimplicial(NormalToricVariety)
 whether a normal toric variety is simplicial
isSmooth(NormalToricVariety)
 whether a normal toric variety is smooth
isSurjective(ToricMap)
 whether a toric map is surjective
isVeryAmple(ToricDivisor)
 whether a torusinvariant Weil divisor is very ample
isWellDefined(NormalToricVariety)
 whether a toric variety is welldefined
isWellDefined(ToricDivisor)
 whether a toric divisor is welldefined
isWellDefined(ToricMap)
 whether a toric map is well defined
kleinschmidt(ZZ,List)
 make any smooth normal toric variety having Picard rank two
latticePoints(ToricDivisor)
 compute the lattice points in the associated polytope
makeSimplicial(NormalToricVariety)
 make a birational simplicial toric variety
makeSmooth(NormalToricVariety)
 make a birational smooth toric variety
making normal toric varieties
 information about the basic constructors
map(NormalToricVariety,NormalToricVariety,Matrix)
 make a torusequivariant map between normal toric varieties
map(NormalToricVariety,NormalToricVariety,ZZ)
 make a torusequivariant map between normal toric varieties
matrix(ToricMap)
 get the underlying map of lattices
max(NormalToricVariety)
 get the maximal cones in the associated fan
monomials(ToricDivisor)
 list the monomials that span the linear series
nefGenerators(NormalToricVariety)
 compute generators of the nef cone
NormalToricVariety
 the class of all normal toric varieties
NormalToricVariety ** NormalToricVariety
 make the Cartesian product of two normal toric varieties
NormalToricVariety ^ Array
 make a canonical projection map
NormalToricVariety ^** ZZ
 make the Cartesian power of a normal toric variety
NormalToricVariety _ Array
 make a canonical inclusion into a product
NormalToricVariety _ ZZ
 make an irreducible torusinvariant divisor
normalToricVariety(Fan)
 make a normal toric variety from a 'Polyhedra' fan
normalToricVariety(List,List)
 make a normal toric variety
normalToricVariety(Matrix)
 make a normal toric variety from a polytope
normalToricVariety(Polyhedron)
 make a normal toric variety from a 'Polyhedra' polyhedron
normalToricVariety(Ring)
 get the associated normal toric variety
OO ToricDivisor
 make the associated rankone reflexive sheaf
orbits(NormalToricVariety)
 make a hashtable indexing the torus orbits (a.k.a. cones in the fan)
orbits(NormalToricVariety,ZZ)
 get a list of the torus orbits (a.k.a. cones in the fan) of a given dimension
picardGroup(NormalToricVariety)
 make the Picard group
picardGroup(ToricMap)
 make the induced map between Picard groups
polytope(ToricDivisor)
 makes the associated 'Polyhedra' polyhedron
projective space
 information about various constructions of projective space
pullback
 make the pullback along a toric map
pullback(ToricMap,CoherentSheaf)
 make the pullback of a coherent sheaf under a toric map
pullback(ToricMap,ToricDivisor)
 make the pullback of a Cartier divisor under a toric map
rays(NormalToricVariety)
 get the rays of the associated fan
resolving singularities
 information about find a smooth proper birational surjection
ring(NormalToricVariety)
 make the total coordinate ring (a.k.a. Cox ring)
sheaf(NormalToricVariety,Module)
 make a coherent sheaf
sheaf(NormalToricVariety,Ring)
 make a coherent sheaf of rings
smallAmpleToricDivisor(ZZ,ZZ)
 get a very ample toric divisor from the database
smoothFanoToricVariety(ZZ,ZZ)
 get a smooth Fano toric variety from database
source(ToricMap)
 get the source of the map
support(ToricDivisor)
 make the list of irreducible divisors with nonzero coefficients
target(ToricMap)
 get the target of the map
todd(CoherentSheaf)
 compute the Todd class of a coherent sheaf
toricBlowup(List,NormalToricVariety,List)
 makes the toricBlowup of a normal toric variety along a torus orbit closure
ToricDivisor
 the class of all torusinvariant Weil divisors
ToricDivisor == ToricDivisor
 equality of toric divisors
toricDivisor(List,NormalToricVariety)
 make a torusinvariant Weil divisor
toricDivisor(NormalToricVariety)
 make the canonical divisor
toricDivisor(Polyhedron)
 make the toric divisor associated to a polyhedron
ToricMap
 the class of all torusequivariant maps between normal toric varieties
ToricMap * ToricMap
 make the composition of two toric maps
ToricMap == ToricMap
 whether to toric maps are equal
toricProjectiveSpace(ZZ)
 make a projective space as a normal toric variety
variety(ToricDivisor)
 get the underlying normal toric variety
vector(ToricDivisor)
 make the vector of coefficients
vertices(ToricDivisor)
 compute the vertices of the associated polytope
weightedProjectiveSpace(List)
 make a weighted projective space
weilDivisorGroup(NormalToricVariety)
 make the group of torusinvariant Weil divisors
weilDivisorGroup(ToricMap)
 make the induced map between groups of Weil divisors
working with divisors
 information about toric divisors and their related groups
working with sheaves
 information about coherent sheaves and total coordinate rings (a.k.a. Cox rings)
working with toric maps
 information about toric maps and the induced operations