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[FTheoryTools] Introduce optional argument generic for literature model constructor #3578

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Apr 10, 2024
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[FTheoryTools] Introduce optional argument generic for literature model constructor #3578

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30 changes: 28 additions & 2 deletions experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -699,8 +699,8 @@ Resolve a model with the index-th resolution that is known.
julia> B3 = projective_space(NormalToricVariety, 3)
Normal toric variety

julia> w = 2 * torusinvariant_prime_divisors(B3)[1]
Torus-invariant, non-prime divisor on a normal toric variety
julia> w = torusinvariant_prime_divisors(B3)[1]
Torus-invariant, prime divisor on a normal toric variety

julia> t = literature_model(arxiv_id = "1109.3454", equation = "3.1", base_space = B3, model_sections = Dict("w" => w), completeness_check = false)
Construction over concrete base may lead to singularity enhancement. Consider computing singular_loci. However, this may take time!
Expand All @@ -709,6 +709,32 @@ Global Tate model over a concrete base -- SU(5)xU(1) restricted Tate model based

julia> t2 = resolve(t, 1)
Partially resolved global Tate model over a concrete base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)

julia> cox_ring(ambient_space(t2))
Multivariate polynomial ring in 12 variables over QQ graded by
x1 -> [1 0 0 0 0 0 0]
x2 -> [0 1 0 0 0 0 0]
x3 -> [0 1 0 0 0 0 0]
x4 -> [0 1 0 0 0 0 0]
x -> [0 0 1 0 0 0 0]
y -> [0 0 0 1 0 0 0]
z -> [0 0 0 0 1 0 0]
e1 -> [0 0 0 0 0 1 0]
e4 -> [0 0 0 0 0 0 1]
e2 -> [-1 -3 -1 1 -1 -1 0]
e3 -> [0 4 1 -1 1 0 -1]
s -> [2 6 -1 0 2 1 1]

julia> w2 = 2 * torusinvariant_prime_divisors(B3)[1]
Torus-invariant, non-prime divisor on a normal toric variety

julia> t3 = literature_model(arxiv_id = "1109.3454", equation = "3.1", base_space = B3, model_sections = Dict("w" => w2), completeness_check = false, generic = true)
Construction over concrete base may lead to singularity enhancement. Consider computing singular_loci. However, this may take time!

Global Tate model over a concrete base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)

julia> t4 = resolve(t3, 1)
Partially resolved global Tate model over a concrete base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
```
"""
function resolve(m::AbstractFTheoryModel, resolution_index::Int)
Expand Down
32 changes: 22 additions & 10 deletions experimental/FTheoryTools/src/LiteratureModels/constructors.jl
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Expand Up @@ -32,6 +32,16 @@ Some literature models require additional parameters to specified to single out
a model from a family of models. Such models can be provided using the optional
argument `model_parameters`, which should be a dictionary such as `Dict("k" => 5)`.

Notice that most F-theory models require the specification of sections of line
bundles. Oftentimes, these sections appear in the singular loci of the models.
Hence, generic sections also mean complicated singular loci. In case those loci
are supposed to be blown up, then taking generic sections results in the most
complicated situation with regard to singularity resolution. With that being said,
we default to simple section consisting of a single monomial unless the optional
argument `generic` is set to `true`. In other words, if you add
`generic = true` to the argument list of `literature_model`, generic sections are
used in the construction and subsequently resolution of the F-theory model in question.

```jldoctest
julia> t = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Expand Down Expand Up @@ -125,17 +135,17 @@ julia> hypersurface_equation_parametrization(h2)
b*w*v^2 - c0*u^4 - c1*u^3*v - c2*u^2*v^2 - c3*u*v^3 + w^2
```
"""
function literature_model(; doi::String="", arxiv_id::String="", version::String="", equation::String="", model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true)
function literature_model(; doi::String="", arxiv_id::String="", version::String="", equation::String="", model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true, generic::Bool = false)
model_dict = _find_model(doi, arxiv_id, version, equation)
return literature_model(model_dict; model_parameters = model_parameters, base_space = base_space, model_sections = model_sections, completeness_check = completeness_check)
return literature_model(model_dict; model_parameters = model_parameters, base_space = base_space, model_sections = model_sections, completeness_check = completeness_check, generic = generic)
end

function literature_model(k::Int; model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true)
function literature_model(k::Int; model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true, generic::Bool = false)
model_dict = _find_model(k)
return literature_model(model_dict; model_parameters = model_parameters, base_space = base_space, model_sections = model_sections, completeness_check = completeness_check)
return literature_model(model_dict; model_parameters = model_parameters, base_space = base_space, model_sections = model_sections, completeness_check = completeness_check, generic = generic)
end

function literature_model(model_dict::Dict{String, Any}; model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true)
function literature_model(model_dict::Dict{String, Any}; model_parameters::Dict{String,<:Any} = Dict{String,Any}(), base_space::FTheorySpace = affine_space(NormalToricVariety, 0), model_sections::Dict{String, <:Any} = Dict{String,Any}(), completeness_check::Bool = true, generic::Bool = false)
#return model_dict
# (1) Deal with model parameters
if haskey(model_dict, "model_parameters")
Expand Down Expand Up @@ -175,7 +185,7 @@ function literature_model(model_dict::Dict{String, Any}; model_parameters::Dict{
end

# Construct the model
model = _construct_literature_model_over_concrete_base(model_dict, base_space, model_sections, completeness_check)
model = _construct_literature_model_over_concrete_base(model_dict, base_space, model_sections, completeness_check, generic)
@vprint :FTheoryModelPrinter 0 "Construction over concrete base may lead to singularity enhancement. Consider computing singular_loci. However, this may take time!\n\n"

# (2b) Construct the model over generic base
Expand Down Expand Up @@ -245,7 +255,7 @@ end
#######################################################

# Constructs literature model over concrete base
function _construct_literature_model_over_concrete_base(model_dict::Dict{String,Any}, base_space::FTheorySpace, model_sections::Dict{String,ToricDivisor}, completeness_check::Bool)
function _construct_literature_model_over_concrete_base(model_dict::Dict{String,Any}, base_space::FTheorySpace, model_sections::Dict{String,ToricDivisor}, completeness_check::Bool, generic::Bool)

# We first create a polynomial ring in which we can read all model sections as polynomials of the defining sections
@req ((model_dict["model_descriptors"]["type"] == "tate") || (model_dict["model_descriptors"]["type"] == "weierstrass") || (model_dict["model_descriptors"]["type"] == "hypersurface")) "Model is not a Tate or Weierstrass model"
Expand All @@ -269,9 +279,11 @@ function _construct_literature_model_over_concrete_base(model_dict::Dict{String,
explicit_model_sections = Dict{String, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}}()
for (key, value) in model_sections
@req is_effective(toric_divisor_class(value)) "Encountered a non-effective model section"
explicit_model_sections[key] = generic_section(toric_line_bundle(value))
# Lead to error when computing singular loci - currently only monomials allowed...
#explicit_model_sections[key] = basis_of_global_sections(toric_line_bundle(value))[end]
if generic
explicit_model_sections[key] = generic_section(toric_line_bundle(value))
else
explicit_model_sections[key] = basis_of_global_sections(toric_line_bundle(value))[end]
end
Comment on lines -273 to +286
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@HereAround HereAround Apr 10, 2024 •
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This is the key change/proposal to make the book example function again. The remainder is cosmetics, including a doc test that will fail if there is a new breaking change to said book example.

end
for (key, value) in internal_model_sections
@req is_effective(toric_divisor_class(value)) "Encountered a non-effective (internal) model section"
Expand Down
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