[ToricSchemes] Fixes to blow up of toric variety from new ray

experimental/Schemes/ToricBlowups/attributes.jl

@@ -47,12 +47,6 @@ index_of_new_ray(bl::ToricBlowdownMorphism) = bl.index_of_new_ray
 
 Return the center of the toric blowdown morphism as ideal sheaf.
 
-Currently (October 2023), ideal sheaves are only supported for
-smooth toric varieties. Hence, there will be instances in which
-the construction of a blowdown morphism succeeds, but the center
-of the blowup, as represented by an ideal sheaf, cannot yet be
-computed.
-
 # Examples
 ```jldoctest
 julia> P3 = projective_space(NormalToricVariety, 3)
@@ -63,7 +57,7 @@ Toric blowdown morphism
 
 julia> center(blow_down_morphism)
 Sheaf of ideals
-  on normal toric variety
+  on normal, smooth toric variety
 with restrictions
   1: Ideal (x_3_1, x_2_1)
   2: Ideal (x_3_2, x_2_2)

experimental/Schemes/ToricBlowups/constructors.jl

@@ -87,14 +87,60 @@ Multivariate polynomial ring in 5 variables over QQ graded by
   x3 -> [0 1]
   x4 -> [1 0]
   e -> [1 -1]
+
+julia> typeof(center(blow_down_morphism))
+Oscar.ToricIdealSheafFromCoxRingIdeal{NormalToricVariety, AbsAffineScheme, Ideal, Map}
+
+julia> Oscar.ideal_in_cox_ring(center(blow_down_morphism))
+Ideal generated by
+  x2
+  x3
+```
+Notice that in the above example, the blowup center is not just an ideal sheaf.
+Rather, it is an ideal sheaf that knows its datum, in the form of an ideal,
+in the Cox ring. Sadly, we cannot always (at least not yet) compute such a datum.
+The following example demonstrates such a case.
+
+# Examples
+```jldoctest
+julia> rs = [1 1; -1 1]
+2×2 Matrix{Int64}:
+  1  1
+ -1  1
+
+julia> max_cones = IncidenceMatrix([[1, 2]])
+1×2 IncidenceMatrix
+[1, 2]
+
+julia> v = normal_toric_variety(max_cones, rs)
+Normal toric variety
+
+julia> bu = blow_up(v, [0, 1])
+Toric blowdown morphism
+
+julia> center(bu)
+Sheaf of ideals
+  on normal, non-smooth toric variety
+with restriction
+  1: Ideal (x_3_1, x_2_1, x_1_1)
+
+julia> typeof(center(bu))
+IdealSheaf{NormalToricVariety, AbsAffineScheme, Ideal, Map}
 ```
 """
 function blow_up(v::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String = "e")
   new_variety = normal_toric_variety(star_subdivision(v, new_ray))
+  @req n_rays(v) != n_rays(new_variety) "New ray already a ray of the given toric variety"
+  if is_smooth(v) == false
+    return ToricBlowdownMorphism(v, new_variety, coordinate_name, new_ray)
+  end
   inx = _get_maximal_cones_containing_vector(polyhedral_fan(v), new_ray)
   old_rays = matrix(ZZ, rays(v))
   cone_generators = matrix(ZZ, [old_rays[i,:] for i in 1:nrows(old_rays) if ray_indices(maximal_cones(v))[inx[1], i]])
-  powers = solve_mixed(ZZMatrix, transpose(cone_generators), transpose(matrix(ZZ, [new_ray])), identity_matrix(ZZ, ncols(old_rays)))
+  powers = solve_non_negative(ZZMatrix, transpose(cone_generators), transpose(matrix(ZZ, [new_ray])))
+  if nrows(powers) != 1
+    return ToricBlowdownMorphism(v, new_variety, coordinate_name, new_ray)
+  end
   gens_S = gens(cox_ring(v))
   variables = [gens_S[i] for i in 1:nrows(old_rays) if ray_indices(maximal_cones(v))[inx[1], i]]
   list_of_gens = [variables[i]^powers[i] for i in 1:length(powers) if powers[i] != 0]

experimental/Schemes/ToricBlowups/methods.jl

@@ -21,7 +21,7 @@ julia> x, y, z = gens(S);
 
 julia> I = ideal_sheaf(P2, ideal([x*y]))
 Sheaf of ideals
-  on normal toric variety
+  on normal, smooth toric variety
 with restrictions
   1: Ideal (x_1_1*x_2_1)
   2: Ideal (x_2_2)

experimental/Schemes/ToricBlowups/types.jl

@@ -8,10 +8,16 @@
 
   toric_morphism::ToricMorphism
   index_of_new_ray::Integer
-  center::ToricIdealSheafFromCoxRingIdeal
+  center::Union{ToricIdealSheafFromCoxRingIdeal, IdealSheaf}
   exceptional_divisor::ToricDivisor
 
   function ToricBlowdownMorphism(v::NormalToricVariety, new_variety::NormalToricVariety, coordinate_name::String, center::ToricIdealSheafFromCoxRingIdeal, new_ray::AbstractVector{<:IntegerUnion})
+    bl = ToricBlowdownMorphism(v, new_variety, coordinate_name, new_ray)
+    bl.center = center
+    return bl
+  end
+
+  function ToricBlowdownMorphism(v::NormalToricVariety, new_variety::NormalToricVariety, coordinate_name::String, new_ray::AbstractVector{<:IntegerUnion})
 
     # Compute position of new ray
     new_rays = matrix(ZZ, rays(new_variety))
@@ -37,13 +43,10 @@
 
     # Construct the toric morphism and construct the object
     bl = toric_morphism(new_variety, identity_matrix(ZZ, ambient_dim(polyhedral_fan(v))), v; check=false)
-    return new{typeof(domain(bl)), typeof(codomain(bl))}(bl, position_new_ray, center)
+    return new{typeof(domain(bl)), typeof(codomain(bl))}(bl, position_new_ray)
   end
 end
 
-#toric_blowdown_morphism(bl::ToricMorphism, new_ray::AbstractVector{<:IntegerUnion}, center::IdealSheaf) = ToricBlowdownMorphism(bl, new_ray, center)
-#toric_blowdown_morphism(Y::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}, coordinate_name::String) = ToricBlowdownMorphism(Y, new_ray, coordinate_name)
-
 
 
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