Construct the toric divisor class associated to a group element of the class group of the normal toric variety v.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, class_group(P2)([1]))
Divisor class on a normal toric variety
toric_divisor_class(v::NormalToricVarietyType, coeffs::Vector{T}) where {T <: IntegerUnion}
Construct the toric divisor class associated to a list of integers which specify an element of the class group of the normal toric variety v.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, class_group(P2)([ZZRingElem(1)]))
Divisor class on a normal toric variety
Construct the toric divisor class associated to the element ... of the class group of the normal toric variety v.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> td = toric_divisor(P2, [1, 2, 3])
Torus-invariant, non-prime divisor on a normal toric variety
julia> tdc = toric_divisor_class(td)
Divisor class on a normal toric variety
Toric divisor classes can be added and subtracted via the usual + and - operators. Moreover, multiplication by scalars from the left is supported for scalars which are integers or of type ZZRingElem.
Determine whether the toric divisor class tdc is effective, that is if a toric divisor in this divisor class is linearly equivalent to an effective toric divisor.
Examples
julia> P2 = projective_space(NormalToricVariety,2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, [1])
Divisor class on a normal toric variety
julia> is_effective(tdc)
true
julia> tdc2 = toric_divisor_class(P2, [-1])
Divisor class on a normal toric variety
julia> is_effective(tdc2)
false
Return the element of the class group corresponding to the toric divisor class tdc.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, class_group(P2)([1]))
Divisor class on a normal toric variety
julia> divisor_class(tdc)
Abelian group element [1]
Return the toric variety on which the toric divisor class tdc is defined.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, class_group(P2)([1]))
Divisor class on a normal toric variety
julia> toric_variety(tdc)
Normal toric variety
Construct a toric divisor corresponding to the toric divisor class tdc.
Examples
julia> P2 = projective_space(NormalToricVariety, 2)
Normal toric variety
julia> tdc = toric_divisor_class(P2, class_group(P2)([1]))
Divisor class on a normal toric variety
julia> toric_divisor(tdc)
Torus-invariant, prime divisor on a normal toric variety