more changes around projectivization

experimental/Schemes/src/elliptic_surface.jl

@@ -426,7 +426,7 @@ function weierstrass_model(X::EllipticSurface)
 
   bundleE = direct_sum([O0, O4, O6])
 
-  P_proj = projectivization(bundleE, var_names=["z", "x", "y"])
+  P_proj = projectivization(bundleE, var_names=[:z, :x, :y])
   P = covered_scheme(P_proj)
   pr = covered_projection_to_base(P_proj)
   @assert has_decomposition_info(default_covering(P))

src/AlgebraicGeometry/Schemes/Sheaves/CoherentSheaves.jl

@@ -1031,7 +1031,7 @@ rings can be provided with `var_names`.
 can be computed. The check for this can be turned off by setting `check=false`.
 """
 function projectivization(E::AbsCoherentSheaf;
-    var_names::Vector{String}=Vector{String}(),
+    var_names::Vector{<:VarNames}=Vector{Symbol}(),
     check::Bool=true
   )
   X = scheme(E)
@@ -1049,15 +1049,15 @@ function projectivization(E::AbsCoherentSheaf;
       F isa FreeMod || error("modules must locally be free")
       r = (rank(F) > r ? rank(F) : r)
     end
-    var_names = ["s$i" for i in 0:r-1]
+    var_names = [Symbol(:s, i) for i in 0:r-1]
   end
 
   for U in patches(C)
     F = E(U)
     F isa FreeMod || error("modules must locally be free")
     r = rank(F)
     length(var_names) >= r || error("number of names for the variables must greater or equal to the local rank of the module")
-    RU = rees_algebra(E(U), var_names=var_names[1:r])
+    RU = rees_algebra(E(U); var_names=var_names[1:r])
     algebras[U] = RU
     SU, _ = grade(RU)
     PU = proj(SU)

src/Rings/ReesAlgebra.jl

@@ -13,17 +13,17 @@ module ``F`` this computes the Rees algebra of ``M`` according to
 [EHU03](@cite)[^2].
 
 !!! note If `check` is set to `true`, the method will check the sufficient
-criterion "``fᵀ : F* → M*`` surjective" to verify that ``f`` is versal.
-Since no general criterion is known, this will abort with an error message
-in the non-affirmative case.
+         criterion "``fᵀ : F* → M*`` surjective" to verify that ``f`` is versal.
+         Since no general criterion is known, this will abort with an error message
+         in the non-affirmative case.
 
 [^1]: A morphism of ``M`` into a free module ``F`` as above is called versal if any other morphism ``g : M → F'`` from ``M`` to another free module ``F'`` factors through ``f``.
 
 [^2]: See arXiv:math/0209187v1 for a free version.
 """
 function rees_algebra(f::ModuleFPHom{<:ModuleFP, <:FreeMod, Nothing};
     check::Bool=true,
-    var_names::Vector{String}=["s$i" for i in 0:ngens(domain(f))-1]
+    var_names::Vector{String}=[Symbol(:s, i) for i in 0:ngens(domain(f))-1]
   )
   if check
     f_dual = dual(f)
@@ -53,7 +53,8 @@ function rees_algebra(f::ModuleFPHom{<:ModuleFP, <:FreeMod, Nothing};
 end
 
 function rees_algebra(M::FreeMod;
-    var_names::Vector{String}=["s$i" for i in 0:ngens(M)-1]
+    check::Bool=true,
+    var_names::Vector{<:VarName}=[Symbol(:s, i) for i in 0:ngens(M)-1]
   )
   R = base_ring(M)
   r = rank(M)
@@ -62,8 +63,8 @@ function rees_algebra(M::FreeMod;
 end
 
 function rees_algebra(M::SubquoModule;
-    var_names::Vector{String}=["s$i" for i in 0:ngens(M)-1],
-    check::Bool=true
+    check::Bool=true,
+    var_names::Vector{String}=[Symbol(:s, i) for i in 0:ngens(M)-1]
   )
   success, p, sigma = is_projective(M)
   if success

test/AlgebraicGeometry/Schemes/CoveredProjectiveSchemes.jl

@@ -71,7 +71,7 @@ end
 
   E = direct_sum([O4, O6, O1])
 
-  X_proj = projectivization(E, var_names=["x", "y", "z"])
+  X_proj = projectivization(E, var_names=[:x, :y, :z])
 
   X = covered_scheme(X_proj)
 

test/AlgebraicGeometry/Schemes/K3.jl

@@ -7,7 +7,7 @@
 
   E = direct_sum([O0, O4, O6])
 
-  X_proj = projectivization(E, var_names=["z", "x", "y"])
+  X_proj = projectivization(E, var_names=[:z, :x, :y])
 
   X = covered_scheme(X_proj)