Added verticality checks for g4 fluxes and changed zero section methods

experimental/FTheoryTools/docs/src/literature.md

@@ -99,6 +99,7 @@ following methods:
 * `has_weighted_resolution_generating_sections(m::AbstractFTheoryModel)`,
 * `has_weighted_resolution_zero_sections(m::AbstractFTheoryModel)`,
 * `has_zero_section(m::AbstractFTheoryModel)`,
+* `has_zero_section_coordinates(m::AbstractFTheoryModel)`,
 * `has_gauge_algebra(m::AbstractFTheoryModel)`,
 * `has_global_gauge_quotients(m::AbstractFTheoryModel)`.
 

experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl

@@ -1013,10 +1013,10 @@ end
 
 
 @doc raw"""
-    zero_section(m::AbstractFTheoryModel)
+    zero_section_coordinates(m::AbstractFTheoryModel)
 
-Return the zero section of the given model.
-If no zero section is known, an error is raised.
+Return the zero section coordinates of the given model.
+If no zero section coordinates are known, an error is raised.
 This information is not typically stored as an attribute for
 Weierstrass and global Tate models, whose zero sections are known.
 
@@ -1026,13 +1026,35 @@ Assuming that the first row of the given grading is the grading under Kbar
 
 Hypersurface model over a not fully specified base
 
-julia> zero_section(h)
+julia> zero_section_coordinates(h)
 3-element Vector{QQMPolyRingElem}:
  0
  1
  0
 ```
 """
+function zero_section_coordinates(m::AbstractFTheoryModel)
+  @req has_zero_section_coordinates(m) "No zero section coordinates stored for this model"
+  return get_attribute(m, :zero_section_coordinates)
+end
+
+
+@doc raw"""
+    zero_section(m::AbstractFTheoryModel)
+
+Return the zero section of a model as a cohomology class in the toric ambient space.
+If no zero section is known, an error is raised.
+This information is not typically stored as an attribute for
+Weierstrass and global Tate models, whose zero sections are known.
+
+```jldoctest; setup = :(Oscar.LazyArtifacts.ensure_artifact_installed("QSMDB", Oscar.LazyArtifacts.find_artifacts_toml(Oscar.oscardir)))
+julia> qsm_model = literature_model(arxiv_id = "1903.00009", model_parameters = Dict("k" => 4))
+Hypersurface model over a concrete base
+
+julia> zero_section(qsm_model)
+Cohomology class on a normal toric variety given by x32 + 2*x33 + 3*x34 + x35 - x36
+```
+"""
 function zero_section(m::AbstractFTheoryModel)
   @req has_zero_section(m) "No zero section stored for this model"
   return get_attribute(m, :zero_section)

experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl

@@ -634,10 +634,18 @@ function set_weighted_resolution_zero_sections(m::AbstractFTheoryModel, vs::Vect
   set_attribute!(m, :weighted_resolution_zero_sections => result)
 end
 
-function set_zero_section(m::AbstractFTheoryModel, desired_value::Vector{String})
+function set_zero_section_coordinates(m::AbstractFTheoryModel, desired_value::Vector{String})
   R, _ = polynomial_ring(QQ, collect(keys(explicit_model_sections(m))), cached = false)
   f = hom(R, cox_ring(base_space(m)), collect(values(explicit_model_sections(m))))
-  set_attribute!(m, :zero_section => [f(eval_poly(l, R)) for l in desired_value])
+  set_attribute!(m, :zero_section_coordinates => [f(eval_poly(l, R)) for l in desired_value])
+end
+
+function set_zero_section(m::AbstractFTheoryModel, desired_value::String)
+  divs = torusinvariant_prime_divisors(ambient_space(m))
+  cohomology_ring(ambient_space(m); check=false)
+  cox_gens = [string(x) for x in gens(cox_ring(ambient_space(m)))]
+  index = findfirst(x -> x==desired_value, cox_gens)
+  set_attribute!(m, :zero_section => cohomology_class(divs[index]))
 end
 
 function set_gauge_algebra(m::AbstractFTheoryModel, algebras::Vector{String})

experimental/FTheoryTools/src/AbstractFTheoryModels/properties.jl

@@ -96,6 +96,7 @@ has_weighted_resolutions(m::AbstractFTheoryModel) = has_attribute(m, :weighted_r
 has_weighted_resolution_generating_sections(m::AbstractFTheoryModel) = has_attribute(m, :weighted_resolution_generating_sections)
 has_weighted_resolution_zero_sections(m::AbstractFTheoryModel) = has_attribute(m, :weighted_resolution_zero_sections)
 has_zero_section(m::AbstractFTheoryModel) = has_attribute(m, :zero_section)
+has_zero_section_coordinates(m::AbstractFTheoryModel) = has_attribute(m, :zero_section_coordinates)
 has_gauge_algebra(m::AbstractFTheoryModel) = has_attribute(m, :gauge_algebra)
 has_global_gauge_quotients(m::AbstractFTheoryModel) = has_attribute(m, :global_gauge_quotients)
 

experimental/FTheoryTools/src/G4Fluxes/properties.jl

@@ -41,14 +41,24 @@ true
   @req ambient_space(m) isa NormalToricVariety "Elementary quantization checks for G4-flux currently supported only for toric ambient space"
 
   # Compute the cohomology class corresponding to the hypersurface equation
-  cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
-
+  if m isa WeierstrassModel
+    cl = toric_divisor_class(ambient_space(m), degree(weierstrass_polynomial(m)))
+  end
+  if m isa GlobalTateModel
+    cl = toric_divisor_class(ambient_space(m), degree(tate_polynomial(m)))
+  end
+  if m isa HypersurfaceModel
+    cl = toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))
+  end
+  cy = polynomial(cohomology_class(cl))
+
   # Now check quantization condition G4 + 1/2 c2 is integral.
   c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))]
 
   # explicitly switched off an expensive test in the following line
   twist_g4 = polynomial(cohomology_class(g4) + 1//2 * chern_class(m, 2; check = false))
 
+
   # now execute elementary checks of the quantization condition
   for i in 1:length(c_ds)
     for j in i:length(c_ds)
@@ -58,3 +68,42 @@ true
   end
   return true
 end
+
+
+@attr Bool function passes_verticality_checks(g4::G4Flux)
+  m = model(g4)
+  @req (m isa WeierstrassModel || m isa GlobalTateModel || m isa HypersurfaceModel) "Verticality checks for  G4-fluxes only supported for Weierstrass, global Tate and hypersurface models"
+  @req base_space(m) isa NormalToricVariety "Verticality checks for G4-flux currently supported only for toric base"
+  @req ambient_space(m) isa NormalToricVariety "Verticality checks for G4-flux currently supported only for toric ambient space"
+  @req has_zero_section(m) "For verticality checks, a model zero section needs to be specified"
+
+
+  # Compute the cohomology class corresponding to the hypersurface equation
+  if m isa WeierstrassModel
+    cl = toric_divisor_class(ambient_space(m), degree(weierstrass_polynomial(m)))
+  end
+  if m isa GlobalTateModel
+    cl = toric_divisor_class(ambient_space(m), degree(tate_polynomial(m)))
+  end
+  if m isa HypersurfaceModel
+    cl = toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))
+  end
+  cy = polynomial(cohomology_class(cl))
+
+  n = length(gens(cox_ring(base_space(m))))
+  c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))[1:n]]
+  zero_sec = zero_section(m)
+
+  # now execute verticality checks
+  for i in 1:n
+    numb = integrate(cohomology_class(ambient_space(m), polynomial(cohomology_class(g4)) * cy * c_ds[i])*zero_sec; check = false)
+    numb!=0 && return false
+  end
+  for i in 1:n
+    for j in i:n
+      numb = integrate(cohomology_class(ambient_space(m), polynomial(cohomology_class(g4)) * cy * c_ds[i] * c_ds[j]); check = false)
+      numb!=0 && return false
+    end
+  end
+  return true
+end

experimental/FTheoryTools/src/LiteratureModels/Models/model1208_2695-1.json

@@ -54,7 +54,7 @@
             [1, 1, 0]
         ],
         "hypersurface_equation": "w^2 + b * v^2 * w - u * (c0 * u^3 + c1 * u^2 * v + c2 * u * v^2 + c3 * v^3)",
-        "zero_section": ["0", "1", "0"],
+        "zero_section_coordinates": ["0", "1", "0"],
         "generating_sections": [["0", "1", "-b"]]
     },
     "birational_models": ["model1208_2695-2.json"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, -1],
             [-1, -1, -1, -1,  0, 0,  1]
         ],
-        "zero_section": ["0", "0", "1"]
+        "zero_section_coordinates": ["0", "0", "1"]
     },
     "associated_models": [
         "model1408_4808-1-WSF.json",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10.json

@@ -62,7 +62,7 @@
             [-1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*e3^6*u^3 + s2*e1^2*e2^3*e3^4*u^2*v + s3*e1^2*e2^2*e3^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*e3^3*u^2*w + s6*e1*e2*e3*u*v*w + s8*u*w^2",
-        "zero_section": ["s4", "1", "1", "1", "-s8", "0"]
+        "zero_section_coordinates": ["s4", "1", "1", "1", "-s8", "0"]
     },
     "associated_models": [
         "model1408_4808-1.json",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 0],
             [-1, -1, -1,  0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + s9^5*(8*s2*s5^2 - 12*s1*s6*s5) + s5^2*s6^2*s9^4)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11.json

@@ -63,7 +63,7 @@
             [ 1,  1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4^4*u^3 + s2*e1*e2^2*e3^2*e4^2*u^2*v + s3*e2^2*e3^3*u*v^2 + s5*e1^2*e2*e4^3*u^2*w + s6*e1*e2*e3*e4*u*v*w + s9*e1*v*w^2",
-        "zero_section": ["1", "0", "s5", "1", "1", "-s5", "1"],
+        "zero_section_coordinates": ["1", "0", "s5", "1", "1", "-s5", "1"],
         "generating_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0, -1, 0, 1, 0],
             [-1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 - 4*s2*s9)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1"],
         "generating_sections": [
             ["1", "s5", "1", "1", "-s9", "0", "1"],
             ["1", "1", "s2", "-s7", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, 0, 0],
             [-1, -1, -1, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "torsion_sections": [
             ["1//12*(s6^2 - 4*s2*s9)", "0", "1"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13.json

@@ -63,7 +63,7 @@
             [1,  1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e5^4*u^3 + s2*e1*e2^2*e3^2*e4^2*e5^2*u^2*v + s3*e2^2*e3^3*e4^4*u*v^2 + s6*e1*e2*e3*e4*e5*u*v*w + s9*e1*v*w^2",
-        "zero_section": ["1", "s1", "1", "1", "1", "-s9", "0", "1"],
+        "zero_section_coordinates": ["1", "s1", "1", "1", "1", "-s9", "0", "1"],
         "torsion_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "1", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14-WSF.json

@@ -55,7 +55,7 @@
             [-1, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 - s5^2*s9^4*( - s6^2 + 4*s5*s7) - 12*s1*s5*s6*s9^5)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s5*e1^2*e2*e4^2*e5^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15-WSF.json

@@ -55,7 +55,7 @@
             [0, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             ["1//12*(8*s2*s5^2*s9^5 - s5^2*s9^4*( - s6^2 + 4*s5*s7))", " -1//2*s2*s5^3*s6*s9^7", "s5*s9^2"]
         ],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*e5^2*v^2*w + s9*e1*e4^2*e5^2*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s2", "-s7", "1", "1", "0", "1"]
         ],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16-WSF.json

@@ -55,7 +55,7 @@
             [-1, 0, 1, 0],
             [-1, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "torsion_sections": [
             ["1//12*s6^2", "1//2*s1*s7*s9", "1"],
             ["1//12*s6^2", "-1//2*s1*s7*s9", "1"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s6*e1*e2*e3*e4*e5*e6*u*v*w + s7*e2*e3^2*e6^3*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1", "1"],
         "torsion_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0", "1"],
             ["1", "s1", "1", "1", "1", "-s9", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1, 0],
             [-1, -1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + 4*(2*s2*(s5^2 - 3*s1*s8) - 3*s1*s5*s6)*s9^5 + ((s6^2 - 4*s5*s7)*s5^2 + 12*(s2^2 + 2*s1*s3)*s8^2 - 4*(4*s3*s5^2 + s2*s6*s5 - 3*s1*(s6^2 + 2*s5*s7))*s8)*s9^4 - 2*s8*( - 4*(s6*s7 + 3*s4*s8)*s5^2 + (s6^3 - 10*s3*s8*s6 + 4*s2*s7*s8)*s5 + 2*s8*(9*s1*s6*s7 + 6*s1*s4*s8 + s2*(s6^2 + 6*s3*s8)))*s9^3 + s8^2*(s6^4 - 2*s5*s7*s6^2 - 8*s5^2*s7^2 + 12*(s3^2 + 2*s2*s4)*s8^2 - 4*(9*s4*s5*s6 - s7*(5*s2*s6 + 6*s1*s7) + s3*(s6^2 + 2*s5*s7))*s8)*s9^2 - 2*s8^3*(12*s3*s4*s8^2 + 2*(s7*(s3*s6 + 4*s2*s7) - 3*s4*(s6^2 + 2*s5*s7))*s8 + s6*s7*(s6^2 - 4*s5*s7))*s9 + s8^4*((s6^2 - 4*s5*s7)*s7^2 + 4*(2*s3*s7 - 3*s4*s6)*s8*s7 + 12*s4^2*s8^2))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0]
         ],
         "hypersurface_equation": "s1*u^3*e1^2 + s2*u^2*v*e1^2 + s3*u*v^2*e1^2 + s4*v^3*e1^2 + s5*u^2*w*e1 + s6*u*v*w*e1 + s7*v^2*w*e1 + s8*u*w^2 + s9*v*w^2",
-        "zero_section": ["s9", "-s8", "1", "0"],
+        "zero_section_coordinates": ["s9", "-s8", "1", "0"],
         "generating_sections": [
             ["-s9", "s8", "s1 * s9^3 - s4 * s8^3 + s3 * s9 * s8^2 - s2 * s9^2 * s8", "s7 * s8^2 - s6 * s9 * s8 + s5 * s9^2"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1, -1, 0, 1, -1, 0],
             [-1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 + 8*s3*s8 - 4*s2*s9)",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e2^2*e1^2*u^3 + s2*e2^2*e1*u^2*v + s3*e2^2*u*v^2 + s5*e2*e1^2*u^2*w + s6*e2*e1*u*v*w + s7*e2*v^2*w + s8*e1^2*u*w^2 + s9*e1*v*w^2",
-        "zero_section": ["s9", "-s8", "1", "1", "0"],
+        "zero_section_coordinates": ["s9", "-s8", "1", "1", "0"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1"],
             ["0", "1", "1", "s7", "-s9"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1],
             [-1, -1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s8^4*(12*s4^2*s8^2 - s7^2*( - s6^2 + 4*s5*s7) + s7*s8*(8*s3*s7 - 12*s4*s6)))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6.json

@@ -63,7 +63,7 @@
             [1,  1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*u^3 + s2*e1^2*e2^3*u^2*v + s3*e1^2*e2^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*u^2*w + s6*e1*e2*u*v*w + s7*e1*v^2*w + s8*u*w^2",
-        "zero_section": ["-s7", "1", "s8", "1", "0"],
+        "zero_section_coordinates": ["-s7", "1", "s8", "1", "0"],
         "generating_sections": [
             ["0", "1", "s4", "1", "-s7"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7-WSF.json

@@ -54,7 +54,7 @@
             [0,  1, -1, 0, 1, -1, 0],
             [-1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2*s7^2 - 4*s5*s7^3 + 8*s3*s7^2*s8 - 12*s3*s6*s7*s9 + 8*s2*s7^2*s9 + 12*s3^2*s9^2)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e3^2*u^2*v + s3*e2*e3^2*u*v^2 + s5*e1^2*e3*u^2*w + s6*e1*e2*e3*u*v*w + s7*e2^2*e3*v^2*w  + s8*e1^2*e2*u*w^2 + s9*e1*e2^2*w^2*v",
-        "zero_section": ["0", "1", "1", "s7", "1", "-s9"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "1", "-s9"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1", "1"],
             ["1", "s5", "-s2", "1", "0", "1"],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 1, -1],
             [-1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*( - s8^4*(s7^2*( - s6^2 + 4*s5*s7) - 8*s3*s7^2*s8))", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-8.json

@@ -63,7 +63,7 @@
             [-1,  1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*e3^2*u^3 + s2*e1^2*e2^3*e3*u^2*v + s3*e1^2*e2^2*u*v^2 + s5*e1*e2^2*e3^2*u^2*w + s6*e1*e2*e3*u*v*w +  s7*e1*v^2*w + s8*e3^2*u*w^2",
-        "zero_section": ["s7", "1", "1", "-s8", "0", "1"],
+        "zero_section_coordinates": ["s7", "1", "1", "-s8", "0", "1"],
         "generating_sections": [
             ["s7", "1", "-s3", "1", "1", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-9-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 1, 0],
             [-1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 - 4*s2*s9)",