Toric Ideal Sheaves (Experimental)
Ideal sheaves on toric varieties are currently in experimental state. Currently, we support the following functionality. Note that, as of October 2023, this is limited to smooth toric varieties.
ideal_sheaf
— Methodideal_sheaf(td::ToricDivisor)
Return the ideal sheaf corresponding to a toric divisor.
Examples
julia> P3 = projective_space(NormalToricVariety, 3)
Normal toric variety
julia> td = toric_divisor(P3, [0, 1, 0, 0])
Torus-invariant, prime divisor on a normal toric variety
julia> ideal_sheaf(td)
Sheaf of ideals
on normal, smooth toric variety
with restrictions
1: ideal(x_2_1)
2: ideal(x_2_2)
3: ideal(1)
4: ideal(x_2_4)
ideal_sheaf
— Methodideal_sheaf(X::NormalToricVariety, I::MPolyIdeal)
Create a sheaf of ideals on a toric variety $X$ from a homogeneous ideal I
in its cox_ring
.
Examples
julia> P3 = projective_space(NormalToricVariety, 3)
Normal toric variety
julia> (x1,x2,x3,x4) = gens(cox_ring(P3));
julia> I = ideal([x2,x3])
Ideal generated by
x2
x3
julia> IdealSheaf(P3, I);