Rename new_ray to exceptional_ray (#4433)

[ToricVarieties] Rename variable new_ray to exceptional_ray

docs/src/AlgebraicGeometry/ToricVarieties/BlowupMorphisms.md

@@ -15,12 +15,12 @@ For this reason, the methods below should be considered experimental.
 
 We focus mainly on toric blowups given by a star subdivision of a
 polyhedral fan along a primitive vector, see 11.1 Star Subdivisions in
-[CLS11](@cite). Below, we refer to this new primitive vector as
-`new_ray`. The main constructor is the following
-- `blow_up(Y::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String)`
+[CLS11](@cite). Below, we refer to this primitive vector as
+`exceptional_ray`. The main constructor is the following
+- `blow_up(Y::NormalToricVariety, exceptional_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String)`
 This will also construct the underlying toric morphism. We can specify
 the name for the coordinate in the Cox ring that is assigned to
-`new_ray` using the optional argument `coordinate_name`.
+`exceptional_ray` using the optional argument `coordinate_name`.
 
 More generally, we can construct a blowup along a closed subscheme given
 by an ideal in the Cox ring or by an ideal sheaf of the corresponding
@@ -47,7 +47,7 @@ Star Subdivisions in [CLS11](@cite). The resulting star subdivision
 leads to a polyhedral fan, or put differently, the blowup is always
 toric:
 ```@docs
-blow_up(v::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String = "e")
+blow_up(v::NormalToricVariety, exceptional_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String = "e")
 ```
 Most generally, we encode the closed subscheme along which we blow up by
 a homogeneous ideal in the Cox ring. Such blowups are often non-toric,
@@ -67,7 +67,7 @@ blow_up(m::NormalToricVariety, I::ToricIdealSheafFromCoxRingIdeal; coordinate_na
 
 ```@docs
 underlying_morphism(bl::ToricBlowupMorphism)
-index_of_new_ray(bl::ToricBlowupMorphism)
+index_of_exceptional_ray(bl::ToricBlowupMorphism)
 center_data(bl::ToricBlowupMorphism)
 center_unnormalized(bl::ToricBlowupMorphism)
 exceptional_prime_divisor(bl::ToricBlowupMorphism)

docs/src/PolyhedralGeometry/fans.md

@@ -58,6 +58,6 @@ rays(PF::PolyhedralFan)
 rays_modulo_lineality(PF::PolyhedralFan)
 primitive_collections(PF::PolyhedralFan)
 star_subdivision(PF::PolyhedralFan, n::Int)
-star_subdivision(PF::PolyhedralFan, new_ray::AbstractVector{<:IntegerUnion})
+star_subdivision(PF::PolyhedralFan, exceptional_ray::AbstractVector{<:IntegerUnion})
 *(PF1::PolyhedralFan{QQFieldElem}, PF2::PolyhedralFan{QQFieldElem})
 ```

experimental/FTheoryTools/src/auxiliary.jl

@@ -468,7 +468,7 @@ function _strict_transform(bd::ToricBlowupMorphism, II::ToricIdealSheafFromCoxRi
     return strict_transform(bd, II)
   end
   S = cox_ring(domain(bd))
-  _e = gen(S, index_of_new_ray(bd))
+  _e = gen(S, index_of_exceptional_ray(bd))
   images = MPolyRingElem[]
   g_list = gens(S)
   g_center = [string(k) for k in symbols(ideal_in_cox_ring(center_unnormalized(bd)))]
@@ -489,7 +489,7 @@ end
 
 function _strict_transform(bd::ToricBlowupMorphism, tate_poly::MPolyRingElem)
   S = cox_ring(domain(bd))
-  _e = gen(S, index_of_new_ray(bd))
+  _e = gen(S, index_of_exceptional_ray(bd))
   g_list = string.(symbols(S))
   g_center = [string(k) for k in gens(ideal_in_cox_ring(center_unnormalized(bd)))]
   position_of_center_variables = [findfirst(==(g), g_list) for g in g_center]

experimental/Schemes/src/Schemes.jl

@@ -44,12 +44,12 @@ export germ_at_point
 export has_du_val_singularities
 export hypersurface_germ
 export ideal_sheaf
-export index_of_new_ray
+export index_of_exceptional_ray
 export is_isolated_singularity
 export intersection_matrix
 export milnor_algebra
 export milnor_number
-export minimal_supercone_coordinates_of_new_ray
+export minimal_supercone_coordinates_of_exceptional_ray
 export point
 export rational_point_coordinates
 export standard_covering

experimental/Schemes/src/ToricBlowups/attributes.jl

@@ -26,9 +26,9 @@ underlying_morphism(bl::ToricBlowupMorphism) = bl.toric_morphism
 
 
 @doc raw"""
-    index_of_new_ray(bl::ToricBlowupMorphism)
+    index_of_exceptional_ray(bl::ToricBlowupMorphism)
 
-Return the index of the new ray used in the construction of the toric
+Return the index of the exceptional ray used in the construction of the toric
 blowup.
 
 # Examples
@@ -39,11 +39,11 @@ Normal toric variety
 julia> f = blow_up(P3, [0, 1, 1])
 Toric blowup morphism
 
-julia> index_of_new_ray(f)
+julia> index_of_exceptional_ray(f)
 5
 ```
 """
-index_of_new_ray(bl::ToricBlowupMorphism) = bl.index_of_new_ray
+index_of_exceptional_ray(bl::ToricBlowupMorphism) = bl.index_of_exceptional_ray
 
 
 @doc raw"""
@@ -102,7 +102,7 @@ function center_unnormalized(bl::ToricBlowupMorphism)
     X = domain(bl)
     S = cox_ring(X)
     x = gens(S)
-    j = index_of_new_ray(bl)
+    j = index_of_exceptional_ray(bl)
     I = ideal(S, x[j])
     II = ideal_sheaf(X, I)
     JJ = pushforward(bl, II)::IdealSheaf
@@ -141,7 +141,7 @@ function exceptional_prime_divisor(bl::ToricBlowupMorphism)
     X = domain(bl)
     S = cox_ring(X)
     x = gens(S)
-    j = index_of_new_ray(bl)
+    j = index_of_exceptional_ray(bl)
     help_list = [i == j ? 1 : 0 for i in 1:ngens(S)]
     td = toric_divisor(X, help_list)
     @assert is_prime(td) "exceptional prime divisor must be prime"

experimental/Schemes/src/ToricBlowups/constructors.jl

@@ -81,10 +81,10 @@ end
 
 
 @doc raw"""
-    blow_up(v::NormalToricVariety, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String)
+    blow_up(v::NormalToricVariety, exceptional_ray::AbstractVector{<:IntegerUnion}; coordinate_name::String)
 
 Blow up the toric variety by subdividing the fan of the variety with the
-provided new ray. This function returns the corresponding morphism.
+provided exceptional ray. This function returns the corresponding morphism.
 
 Note that this ray must be a primitive element in the lattice Z^d, with
 d the dimension of the fan. In particular, it is currently impossible to
@@ -157,24 +157,24 @@ julia> typeof(center_unnormalized(f))
 IdealSheaf{NormalToricVariety, AbsAffineScheme, Ideal, Map}
 ```
 """
-function blow_up(v::NormalToricVarietyType, new_ray::AbstractVector{<:IntegerUnion}; coordinate_name::Union{String, Nothing} = nothing)
+function blow_up(v::NormalToricVarietyType, exceptional_ray::AbstractVector{<:IntegerUnion}; coordinate_name::Union{String, Nothing} = nothing)
   coordinate_name = _find_blowup_coordinate_name(v, coordinate_name)
-  new_variety = normal_toric_variety(star_subdivision(v, new_ray))
+  blown_up_variety = normal_toric_variety(star_subdivision(v, exceptional_ray))
   if is_smooth(v) == false
-    return ToricBlowupMorphism(v, new_variety, coordinate_name, new_ray, new_ray)
+    return ToricBlowupMorphism(v, blown_up_variety, coordinate_name, exceptional_ray, exceptional_ray)
   end
-  inx = _get_maximal_cones_containing_vector(polyhedral_fan(v), new_ray)
+  inx = _get_maximal_cones_containing_vector(polyhedral_fan(v), exceptional_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_non_negative(ZZMatrix, transpose(cone_generators), transpose(matrix(ZZ, [new_ray])))
+  powers = solve_non_negative(ZZMatrix, transpose(cone_generators), transpose(matrix(ZZ, [exceptional_ray])))
   if nrows(powers) != 1
-    return ToricBlowupMorphism(v, new_variety, coordinate_name, new_ray, new_ray)
+    return ToricBlowupMorphism(v, blown_up_variety, coordinate_name, exceptional_ray, exceptional_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]
   center_unnormalized = ideal_sheaf(v, ideal([variables[i]^powers[i] for i in 1:length(powers) if powers[i] != 0]))
-  return ToricBlowupMorphism(v, new_variety, coordinate_name, new_ray, new_ray, center_unnormalized)
+  return ToricBlowupMorphism(v, blown_up_variety, coordinate_name, exceptional_ray, exceptional_ray, center_unnormalized)
 end
 
 @doc raw"""
@@ -212,10 +212,10 @@ function blow_up(v::NormalToricVarietyType, n::Int; coordinate_name::Union{Strin
   coordinate_name = _find_blowup_coordinate_name(v, coordinate_name)
   gens_S = gens(cox_ring(v))
   center_unnormalized = ideal_sheaf(v, ideal([gens_S[i] for i in 1:number_of_rays(v) if cones(v)[n,i]]))
-  new_variety = normal_toric_variety(star_subdivision(v, n))
+  blown_up_variety = normal_toric_variety(star_subdivision(v, n))
   rays_of_variety = matrix(ZZ, rays(v))
-  new_ray = vec(sum([rays_of_variety[i, :] for i in 1:number_of_rays(v) if cones(v)[n, i]]))
-  return ToricBlowupMorphism(v, new_variety, coordinate_name, new_ray, new_ray, center_unnormalized)
+  exceptional_ray = vec(sum([rays_of_variety[i, :] for i in 1:number_of_rays(v) if cones(v)[n, i]]))
+  return ToricBlowupMorphism(v, blown_up_variety, coordinate_name, exceptional_ray, exceptional_ray, center_unnormalized)
 end
 
 
@@ -274,11 +274,11 @@ function blow_up(v::NormalToricVarietyType, I::MPolyIdeal; coordinate_name::Unio
   indices = [findfirst(==(x), gens(cox)) for x in gens(I)]
   if all(!isnothing, indices)
     rs = matrix(ZZ, rays(v))
-    new_ray = vec(sum(rs[index, :] for index in indices))
-    new_ray = new_ray ./ gcd(new_ray)
-    new_variety = normal_toric_variety(star_subdivision(v, new_ray))
+    exceptional_ray = vec(sum(rs[index, :] for index in indices))
+    exceptional_ray = exceptional_ray ./ gcd(exceptional_ray)
+    blown_up_variety = normal_toric_variety(star_subdivision(v, exceptional_ray))
     center_unnormalized = ideal_sheaf(v, I)
-    return ToricBlowupMorphism(v, new_variety, coordinate_name, new_ray, I, center_unnormalized)
+    return ToricBlowupMorphism(v, blown_up_variety, coordinate_name, exceptional_ray, I, center_unnormalized)
   else
     return _generic_blow_up(v, I)
   end

experimental/Schemes/src/ToricBlowups/methods.jl

@@ -43,9 +43,9 @@ function strict_transform(f::ToricBlowupMorphism, I::MPolyIdeal)
   X = codomain(f)
   @req !has_torusfactor(X) "Only implemented when there are no torus factors"
   S = cox_ring(domain(f))
-  new_var = S[index_of_new_ray(f)]
+  exceptional_var = S[index_of_exceptional_ray(f)]
   J = cox_ring_module_homomorphism(f, I)
-  return saturation(J, ideal(S, new_var))
+  return saturation(J, ideal(S, exceptional_var))
 end
 
 @doc raw"""
@@ -139,9 +139,9 @@ function strict_transform_with_index(f::ToricBlowupMorphism, I::MPolyIdeal)
   @req !has_torusfactor(X) "Only implemented when there are no torus factors"
   @req is_smooth(X) "Only implemented when the fan is smooth"
   S = cox_ring(domain(f))
-  new_var = S[index_of_new_ray(f)]
+  exceptional_var = S[index_of_exceptional_ray(f)]
   J = total_transform(f, I)
-  return saturation_with_index(J, ideal(new_var))
+  return saturation_with_index(J, ideal(exceptional_var))
 end
 
 @doc raw"""
@@ -158,7 +158,7 @@ corresponding to the ray $\rho$ and where $d = 0$ if $\rho$ belongs to
 the fan of $X$ and $d = \lceil a \cdot p \rceil$ otherwise, where $a$ is
 the exponent vector of $g$, $p$ is the minimal supercone coordinate
 vector of $v$ in the fan of $X$, as returned by
-`minimal_supercone_coordinates_of_new_ray(X, v)`, and where $(\cdot)$
+`minimal_supercone_coordinates_of_exceptional_ray(X, v)`, and where $(\cdot)$
 denotes the scalar product.
 
 The $\mathbb{C}$-module homomorphism $\Phi$ sends homogeneous ideals to
@@ -195,8 +195,8 @@ function cox_ring_module_homomorphism(f::ToricBlowupMorphism, g::MPolyDecRingEle
   S_vars = elem_type(S)[S[i] for i in 1:nvars(S)]
 
   nvars(R) == nvars(S) && return hom(R, S, S_vars)(g)
-  ps = minimal_supercone_coordinates_of_new_ray(f)
-  exceptional_var = S[index_of_new_ray(f)]
+  ps = minimal_supercone_coordinates_of_exceptional_ray(f)
+  exceptional_var = S[index_of_exceptional_ray(f)]
   make_S_term(c, exps) = c*prod(map(^, S_vars, exps))
   coeff_exps = collect(zip(coefficients(g), exponents(g)))
   h = S(0)
@@ -213,7 +213,7 @@ function cox_ring_module_homomorphism(f::ToricBlowupMorphism, I::MPolyIdeal)
 end
 
 @doc raw"""
-    minimal_supercone_coordinates_of_new_ray(f::ToricBlowupMorphism) -> Vector{QQFieldElem}
+    minimal_supercone_coordinates_of_exceptional_ray(f::ToricBlowupMorphism) -> Vector{QQFieldElem}
 
 Let $f\colon Y \to X$ be the toric blowup corresponding to a star
 subdivision along a ray with minimal generator $v$.
@@ -228,15 +228,15 @@ Normal toric variety
 julia> f = blow_up(X, [2, 3])
 Toric blowup morphism
 
-julia> minimal_supercone_coordinates_of_new_ray(f)
+julia> minimal_supercone_coordinates_of_exceptional_ray(f)
 2-element Vector{QQFieldElem}:
  2
  3
 ```
 """
-@attr Vector{QQFieldElem} function minimal_supercone_coordinates_of_new_ray(f::ToricBlowupMorphism)
+@attr Vector{QQFieldElem} function minimal_supercone_coordinates_of_exceptional_ray(f::ToricBlowupMorphism)
   PF = polyhedral_fan(codomain(f))
-  v = rays(domain(f))[index_of_new_ray(f), :][1]
+  v = rays(domain(f))[index_of_exceptional_ray(f), :][1]
   v_ZZ = primitive_generator(v)
   return minimal_supercone_coordinates(PF, v_ZZ)
 end

experimental/Schemes/src/ToricBlowups/types.jl

@@ -18,21 +18,24 @@
 } <: AbsSimpleBlowupMorphism{DomainType, CodomainType, ToricBlowupMorphism}
 
   toric_morphism::ToricMorphism
-  index_of_new_ray::Integer
+  index_of_exceptional_ray::Integer
   center_data::CenterDataType
   center_unnormalized::CenterUnnormalizedType
   exceptional_prime_divisor::ToricDivisor
 
-  function _toric_blowup_morphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, new_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType) where CenterDataType <: Union{
+  function _toric_blowup_morphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, exceptional_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType) where CenterDataType <: Union{
     AbstractVector{<:IntegerUnion},
     MPolyIdeal,
     ToricIdealSheafFromCoxRingIdeal,
     IdealSheaf,
   }
-    # Compute position of new ray
+    # Compute position of exceptional ray
     new_rays = matrix(ZZ, rays(new_variety))
-    position_new_ray = findfirst(i->new_ray==new_rays[i,:], 1:n_rays(new_variety))
-    @req position_new_ray !== nothing "Could not identify position of new ray"
+    position_exceptional_ray = findfirst(
+      i->exceptional_ray==new_rays[i,:],
+      1:n_rays(new_variety)
+    )
+    @req position_exceptional_ray !== nothing "Could not identify position of exceptional ray"
 
     # Set variable names of the new variety
     old_vars = string.(symbols(cox_ring(v)))
@@ -54,22 +57,22 @@
 
     # Construct the toric morphism and construct the object
     bl_toric = toric_morphism(new_variety, identity_matrix(ZZ, ambient_dim(polyhedral_fan(v))), v; check=false)
-    return bl_toric, position_new_ray, center_data
+    return bl_toric, position_exceptional_ray, center_data
   end
 
-  function ToricBlowupMorphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, new_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType, center_unnormalized::ToricIdealSheafFromCoxRingIdeal) where CenterDataType <: Union{
+  function ToricBlowupMorphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, exceptional_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType, center_unnormalized::ToricIdealSheafFromCoxRingIdeal) where CenterDataType <: Union{
     AbstractVector{<:IntegerUnion},
     MPolyIdeal,
     ToricIdealSheafFromCoxRingIdeal,
     IdealSheaf,
   }
-    bl_toric, position_new_ray, center_data = _toric_blowup_morphism(v, new_variety, coordinate_name, new_ray, center_data)
+    bl_toric, position_exceptional_ray, center_data = _toric_blowup_morphism(v, new_variety, coordinate_name, exceptional_ray, center_data)
     bl = new{
       typeof(domain(bl_toric)),
       typeof(codomain(bl_toric)),
       typeof(center_data),
       typeof(center_unnormalized),
-    }(bl_toric, position_new_ray, center_data, center_unnormalized)
+    }(bl_toric, position_exceptional_ray, center_data, center_unnormalized)
     if has_attribute(v, :has_torusfactor)
       set_attribute!(bl, :has_torusfactor, has_torusfactor(v))
     end
@@ -79,19 +82,19 @@
     return bl
   end
 
-  function ToricBlowupMorphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, new_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType) where CenterDataType <: Union{
+  function ToricBlowupMorphism(v::NormalToricVarietyType, new_variety::NormalToricVarietyType, coordinate_name::String, exceptional_ray::AbstractVector{<:IntegerUnion}, center_data::CenterDataType) where CenterDataType <: Union{
     AbstractVector{<:IntegerUnion},
     MPolyIdeal,
     ToricIdealSheafFromCoxRingIdeal,
     IdealSheaf,
   }
-    bl_toric, position_new_ray, center_data = _toric_blowup_morphism(v, new_variety, coordinate_name, new_ray, center_data)
+    bl_toric, position_exceptional_ray, center_data = _toric_blowup_morphism(v, new_variety, coordinate_name, exceptional_ray, center_data)
     bl = new{
       typeof(domain(bl_toric)),
       typeof(codomain(bl_toric)),
       typeof(center_data),
       IdealSheaf{typeof(v), AbsAffineScheme, Ideal, Map},
-    }(bl_toric, position_new_ray, center_data)
+    }(bl_toric, position_exceptional_ray, center_data)
     if has_attribute(v, :has_torusfactor)
       set_attribute!(bl, :has_torusfactor, has_torusfactor(v))
     end