NormalToricVarieties : Index
- - ToricDivisor -- perform arithmetic on toric divisors
- affineSpace -- make an affine space
- affineSpace(..., CoefficientRing => ...) -- make an affine space
- affineSpace(..., Variable => ...) -- make an affine space
- affineSpace(ZZ) -- make an affine space
- Basic invariants and properties of normal toric varieties
- blowup -- makes the blowup of a normal toric variety along a torus orbit closure
- blowup(List,NormalToricVariety) -- makes the blowup of a normal toric variety along a torus orbit closure
- blowup(List,NormalToricVariety,List) -- makes the blowup of a normal toric variety along a torus orbit closure
- cartierDivisorGroup -- compute the group of torus-invariant Cartier divisors
- cartierDivisorGroup(NormalToricVariety) -- compute the group of torus-invariant Cartier divisors
- classGroup -- make the class group
- classGroup(NormalToricVariety) -- make the class group
- cotangentSheaf(NormalToricVariety) -- make the sheaf of Zariski 1-forms
- Cox ring -- make the total coordinate ring (a.k.a. Cox ring)
- dim(NormalToricVariety) -- get the dimension of a normal toric variety
- 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
- fromCDivToPic -- get the map from Cartier divisors to the Picard group
- fromCDivToPic(NormalToricVariety) -- get the map from Cartier divisors to the Picard group
- fromCDivToWDiv -- get the map from Cartier divisors to Weil divisors
- fromCDivToWDiv(NormalToricVariety) -- get the map from Cartier divisors to Weil divisors
- fromPicToCl -- get the map from Picard group to class group
- fromPicToCl(NormalToricVariety) -- get the map from Picard group to class group
- fromWDivToCl -- get the map from the group of Weil divisors to the 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
- HH^ZZ(NormalToricVariety,SheafOfRings) -- compute the cohomology of a coherent sheaf
- hirzebruchSurface -- make a Hirzebruch surface
- hirzebruchSurface(..., CoefficientRing => ...) -- make a Hirzebruch surface
- hirzebruchSurface(..., Variable => ...) -- make a Hirzebruch surface
- hirzebruchSurface(ZZ) -- make a Hirzebruch surface
- ideal(NormalToricVariety) -- make the irrelevant ideal
- isAmple -- whether a torus-invariant Weil divisor is ample
- isAmple(ToricDivisor) -- whether a torus-invariant Weil divisor is ample
- isCartier -- whether a torus-invariant Weil divisor is Cartier
- isCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is Cartier
- isComplete(NormalToricVariety) -- whether a toric variety is complete
- isDegenerate -- whether a toric variety is degenerate
- isDegenerate(NormalToricVariety) -- whether a toric variety is degenerate
- isEffective -- whether a torus-invariant Weil divisor is effective
- isEffective(ToricDivisor) -- whether a torus-invariant Weil divisor is effective
- isFano -- whether a normal toric variety is Fano
- isFano(NormalToricVariety) -- whether a normal toric variety is Fano
- isNef -- whether a torus-invariant Weil divisor is nef
- isNef(ToricDivisor) -- whether a torus-invariant Weil divisor is nef
- isProjective -- whether a toric variety is projective
- isProjective(NormalToricVariety) -- whether a toric variety is projective
- isQQCartier -- whether a torus-invariant Weil divisor is QQ-Cartier
- 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
- 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
- kleinschmidt -- make a smooth normal toric variety with Picard rank two
- kleinschmidt(..., CoefficientRing => ...) -- make a smooth normal toric variety with Picard rank two
- kleinschmidt(..., Variable => ...) -- make a smooth normal toric variety with Picard rank two
- kleinschmidt(ZZ,List) -- make a smooth normal toric variety with Picard rank two
- latticePoints(ToricDivisor) -- compute the lattice points in the associated polytope
- makeSimplicial -- make a simplicial toric variety
- makeSimplicial(..., Strategy => ...) -- make a simplicial toric variety
- makeSimplicial(NormalToricVariety) -- make a simplicial toric variety
- makeSmooth -- make a birational smooth toric variety
- makeSmooth(..., Strategy => ...) -- make a birational smooth toric variety
- makeSmooth(NormalToricVariety) -- make a birational smooth toric variety
- Making normal toric varieties
- max(NormalToricVariety) -- get the maximal cones in the associated fan
- monomialIdeal(NormalToricVariety) -- make the irrelevant ideal
- nefGenerators -- compute generators of the nef cone
- nefGenerators(NormalToricVariety) -- compute generators of the nef cone
- NormalToricVarieties -- package for working with normal toric varieties
- NormalToricVariety -- the class of all normal toric varieties
- normalToricVariety -- make a normal toric variety
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of normal toric varieties
- NormalToricVariety ^** ZZ -- make the Cartesian power of a normal toric variety
- NormalToricVariety _ ZZ -- make an irreducible torus-invariant divisor
- normalToricVariety(..., CoefficientRing => ...) -- make a normal toric variety
- normalToricVariety(..., MinimalGenerators => ...) -- make a normal toric variety from a polytope
- normalToricVariety(..., Variable => ...) -- make a normal toric variety
- normalToricVariety(..., WeilToClass => ...) -- make a normal toric variety
- 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
- normalToricVariety(ToricDivisor) -- get the underlying normal toric variety
- OO _ NormalToricVariety -- make a coherent sheaf of rings
- OO ToricDivisor -- make the associated rank-one reflexive sheaf
- orbits -- make a hashtable indexing the torus orbits
- orbits(NormalToricVariety) -- make a hashtable indexing the torus orbits
- orbits(NormalToricVariety,ZZ) -- get a list of the torus orbits of a given dimension
- picardGroup -- make the Picard group
- picardGroup(NormalToricVariety) -- make the Picard group
- polytope(ToricDivisor) -- makes the associated 'Polyhedra' polyhedron
- projectiveSpace -- make a projective space
- projectiveSpace(..., CoefficientRing => ...) -- make a projective space
- projectiveSpace(..., Variable => ...) -- make a projective space
- projectiveSpace(ZZ) -- make a projective space
- rays(NormalToricVariety) -- get the rays of the associated fan
- Resolution of singularities
- ring(NormalToricVariety) -- make the total coordinate ring (a.k.a. Cox ring)
- sheaf(NormalToricVariety) -- make a coherent sheaf of rings
- sheaf(NormalToricVariety,Module) -- make a coherent sheaf
- sheaf(NormalToricVariety,Ring) -- make a coherent sheaf of rings
- smallAmpleToricDivisor -- get a very ample toric divisor from the database
- smallAmpleToricDivisor(..., CoefficientRing => ...) -- get a very ample toric divisor from the database
- smallAmpleToricDivisor(..., Variable => ...) -- get a very ample toric divisor from the database
- smallAmpleToricDivisor(..., WeilToClass => ...) -- get a very ample toric divisor from the database
- smallAmpleToricDivisor(ZZ,ZZ) -- get a very ample toric divisor from the database
- smoothFanoToricVariety -- get a smooth Fano toric variety from database
- smoothFanoToricVariety(..., CoefficientRing => ...) -- get a smooth Fano toric variety from database
- smoothFanoToricVariety(..., Variable => ...) -- get a smooth Fano toric variety from database
- smoothFanoToricVariety(ZZ,ZZ) -- get a smooth Fano toric variety from database
- support(ToricDivisor) -- make the list of irreducible divisors with nonzero coefficients
- ToricDivisor -- the class of all torus-invariant Weil divisors
- toricDivisor -- make a torus-invariant Weil divisor
- ToricDivisor + ToricDivisor -- perform arithmetic on toric divisors
- ToricDivisor - ToricDivisor -- perform arithmetic on toric divisors
- ToricDivisor == ToricDivisor -- equality of toric divisors
- toricDivisor(..., CoefficientRing => ...) -- make the toric divisor associated to a polyhedron
- toricDivisor(..., Variable => ...) -- make the toric divisor associated to a polyhedron
- toricDivisor(..., WeilToClass => ...) -- make the toric divisor associated to a polyhedron
- 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
- Total coordinate rings and coherent sheaves
- variety(Ring) -- get the associated 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 -- make a weighted projective space
- weightedProjectiveSpace(..., CoefficientRing => ...) -- make a weighted projective space
- weightedProjectiveSpace(..., Variable => ...) -- make a weighted projective space
- weightedProjectiveSpace(List) -- make a weighted projective space
- weilDivisorGroup -- make the group of torus-invariant Weil divisors
- weilDivisorGroup(NormalToricVariety) -- make the group of torus-invariant Weil divisors
- WeilToClass -- make a normal toric variety
- Working with divisors and their associated groups
- ZZ * ToricDivisor -- perform arithmetic on toric divisors