[FTheoryTools] Add check for Calabi-Yau condition

experimental/FTheoryTools/docs/src/generalities.md

@@ -69,6 +69,7 @@ euler_characteristic(m::AbstractFTheoryModel; check::Bool = true)
 
 ```@docs
 is_base_space_fully_specified(m::AbstractFTheoryModel)
+is_calabi_yau(m::AbstractFTheoryModel; check::Bool = true)
 is_partially_resolved(m::AbstractFTheoryModel)
 verify_euler_characteristic_from_hodge_numbers(m::AbstractFTheoryModel; check::Bool = true)
 ```

experimental/FTheoryTools/src/AbstractFTheoryModels/properties.jl

@@ -149,3 +149,34 @@ function verify_euler_characteristic_from_hodge_numbers(m::AbstractFTheoryModel;
   set_attribute!(m, :verify_euler_characteristic_from_hodge_numbers, h)
   return h
 end
+
+
+@doc raw"""
+    is_calabi_yau(m::AbstractFTheoryModel; check::Bool = true)
+
+Verify if the first Chern class of the tangent bundle of the F-theory geometry
+$Y_n$ vanishes. If so, this confirms that this geometry is indeed Calabi-Yau,
+as required by the reasoning of F-theory.
+
+The implemented algorithm works for hypersurface, Weierstrass and global Tate models,
+which are defined in a toric ambient space. It expresses $c_1(Y_n)$ as the restriction
+of a cohomology class $h$ on the toric ambient space. This in turn requires that the
+toric ambient space is simplicial and complete. We provide a switch to turn off 
+these computationally very demanding checks. This is demonstrated in the example below.
+
+```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> is_calabi_yau(qsm_model, check = false)
+true
+```
+"""
+function is_calabi_yau(m::AbstractFTheoryModel; check::Bool = true)
+  @req (m isa WeierstrassModel || m isa GlobalTateModel || m isa HypersurfaceModel) "Verification of Euler characteristic of F-theory model supported for Weierstrass, global Tate and hypersurface models only"
+  @req base_space(m) isa NormalToricVariety "Verification of Euler characteristic of F-theory model currently supported only for toric base"
+  @req ambient_space(m) isa NormalToricVariety "Verification of Euler characteristic of F-theory model currently supported only for toric ambient space"
+  return get_attribute!(m, :is_calabi_yau) do
+    return is_trivial(chern_class(m, 1, check = check))
+  end
+end

experimental/FTheoryTools/src/exports.jl

@@ -111,6 +111,7 @@ export hypersurface_model
 export indices_of_trivial_ci_curves
 export irrelevant_ideal
 export is_base_space_fully_specified
+export is_calabi_yau
 export is_partially_resolved
 export journal_doi
 export journal_link