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[FTheoryTools] Remove unused struct for QSM models
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experimental/FTheoryTools/src/exports.jl

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@@ -5,7 +5,6 @@ export FamilyOfG4Fluxes
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export FamilyOfSpaces
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export GlobalTateModel
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export HypersurfaceModel
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export QSMModel
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export WeierstrassModel
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export _blowup_global
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export _blowup_global_sequence

experimental/FTheoryTools/src/types.jl

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@@ -153,85 +153,9 @@ end
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end
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##############################################################################
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# 3 Struct for Quadrillion F-theory Standard Models when read in from database
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##############################################################################
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struct QSMModel
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# Information about the polytope underlying the F-theory QSM.
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vertices::Vector{Vector{QQFieldElem}}
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poly_index::Int
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# We build toric 3-fold from triangulating the lattice points in said polytope.
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# Oftentimes, there are a lot of such triangulations (up to 10^15 for the case at hand), which we cannot
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# hope to enumerate in a reasonable time in a computer. The following gives us metadata, to gauge how hard
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# this triangulation task is. First, the boolean triang_quick tells if we can hope to enumerate all
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# triangulations in a reasonable time. This in turn is linked to the question if we can find
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# fine regular triangulations of all facets, the difficulty of which scales primarily with the number of
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# lattice points. Hence, we also provide the maximal number of lattice points in a facet of the polytope in question
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# in the integer max_lattice_pts_in_facet. On top of this, an estimate for the total number of triangulations
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# is provided by the big integer estimated_number_oftriangulations. This estimate is exact if triang_quick = true.
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triang_quick::Bool
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max_lattice_pts_in_facet::Int
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estimated_number_of_triangulations::Int
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# We select one of the many triangulations, construct a 3d toric base B3 and thereby the hypersurface model in question,
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# that is then the key object of study of this F-theory construction.
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hs_model::HypersurfaceModel
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# As per usual, topological data of this geometry is important. Key is the triple intersection number of the
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# anticanonical divisor of the 3-dimensional toric base, as well as its Hodge numbers.
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Kbar3::Int
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h11::Int
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h12::Int
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h13::Int
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h22::Int
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# Recall that B3 is 3-dimensional toric variety. Let s in H^0(B3, Kbar_B3), then V(s) is a K3-surface.
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# Moreover, let xi the coordinates of the Cox ring of B3. Then V(xi) is a divisor in B3.
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# Furthermore, Ci = V(xi) cap V(s) is a divisor in the K3-surface V(s). We study these curves Ci in large detail.
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# Here is some information about these curves:
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genus_ci::Dict{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}, Int}
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degree_of_Kbar_of_tv_restricted_to_ci::Dict{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}, Int}
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intersection_number_among_ci_cj::Matrix{Int}
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index_facet_interior_divisors::Vector{Int}
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intersection_number_among_nontrivial_ci_cj::Matrix{Int}
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# The collection of the Ci form a nodal curve. To every nodal curve one can associate a (dual) graph. In this graph,
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# every irreducible component of the nodal curve becomes a node/vertex of the dual graph, and every
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# nodal singularity of the nodal curve turns into an edge of the dual graph. Here this is rather simple.
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# Every Ci above is an irreducible component of the nodal curve in question and the topological intersection numbers
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# among the Ci tell us how many nodal singularities link the Ci. Hence, we construct the dual graph as follows:
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# 1. View the Ci as nodes of an undirected graph G.
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# 2. If the top. intersection number of Ci and Cj is zero, there is no edge between the nodes of G corresponding to Ci and Cj.
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# 3. If the top. intersection number of Ci and Cj is n (> 0), then there are n edges between the nodes of G corresponding to Ci and Cj.
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# The following lists the information about this dual graph.
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# Currently, we cannot label the nodes/vertices of a OSCAR graph. However, it is important to remember what vertex/node in the
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# dual graph corresponds to which geometric locus V(xi, s). Therefore, we keep the labels that link the node of the OSCAR graph
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# to the geometric loci V(xi, s) in the vector components_of_dual_graph::Vector{String}. At least for now.
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# Should it ever be possible (favorable?) to directly attach these labels to the graph, one can remove components_of_dual_graph.
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dual_graph::Graph{Undirected}
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components_of_dual_graph::Vector{String}
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degree_of_Kbar_of_tv_restricted_to_components_of_dual_graph::Dict{String, Int64}
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genus_of_components_of_dual_graph::Dict{String, Int64}
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# In our research, we conduct certain combinatoric computations based on this graph, the data in
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# degree_of_Kbar_of_tv_restricted_to_components_of_dual_graph, genus_of_components_of_dual_graph and a bit more meta data
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# that is not currently included (yet). These computations are hard. It turns out, that one can replace the graph with another
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# graph, so that the computations are easier (a.k.a. the runtimes are a lot shorter). In a nutshell, this means to remove
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# a lot of nodes, and adjust the edges accordingly. Let me not go into more details here. A full description can e.g. be found in
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# https://arxiv.org/abs/2104.08297 and the follow-up papers thereof. Here we collect the information of said simplified graph,
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# by mirroring the strategy for the above dual graph.
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simplified_dual_graph::Graph{Undirected}
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components_of_simplified_dual_graph::Vector{String}
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degree_of_Kbar_of_tv_restricted_to_components_of_simplified_dual_graph::Dict{String, Int64}
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genus_of_components_of_simplified_dual_graph::Dict{String, Int64}
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end
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################################################
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# 4: The julia type for G4-fluxes
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# 3: The julia type for G4-fluxes
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################################################
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@attributes mutable struct G4Flux
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################################################
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# 5 The julia type for a family of G4-fluxes
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# 4 The julia type for a family of G4-fluxes
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################################################
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@attributes mutable struct FamilyOfG4Fluxes

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