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 torus-invariant 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 1-forms
• ctop(CoherentSheaf) -- compute the top Chern class of a coherent sheaf
• degree(ToricDivisor) -- make the degree of the associated rank-one 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 torus-invariant Weil divisor is ample
• isCartier(ToricDivisor) -- whether a torus-invariant 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 torus-invariant 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 torus-invariant Weil divisor is nef
• isProjective(NormalToricVariety) -- whether a toric variety is projective
• isProper(ToricMap) -- whether a toric map is proper
• isQQCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is QQ-Cartier
• 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 torus-invariant Weil divisor is very ample
• isWellDefined(NormalToricVariety) -- whether a toric variety is well-defined
• isWellDefined(ToricDivisor) -- whether a toric divisor is well-defined
• 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 torus-equivariant map between normal toric varieties
• map(NormalToricVariety,NormalToricVariety,ZZ) -- make a torus-equivariant 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 torus-invariant 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 rank-one 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(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 torus-invariant Weil divisors
• ToricDivisor == ToricDivisor -- equality of toric divisors
• toricDivisor(List,NormalToricVariety) -- make a torus-invariant Weil divisor
• toricDivisor(NormalToricVariety) -- make the canonical divisor
• toricDivisor(Polyhedron) -- make the toric divisor associated to a polyhedron
• ToricMap -- the class of all torus-equivariant 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 torus-invariant 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