Intersection theory: fix issue #4512 and more

experimental/IntersectionTheory/docs/src/AbstractBundles.md

@@ -5,6 +5,10 @@ DocTestSetup = Oscar.doctestsetup()
 
 # Abstract Bundles
 
+## Types
+
+The OSCAR type for abstract varieties is `AbstractBundle`.
+
 ## Constructors
 
 ```@docs

experimental/IntersectionTheory/docs/src/AbstractVarieties.md

@@ -7,7 +7,7 @@ DocTestSetup = Oscar.doctestsetup()
 
 ## Types
 
-AbsVariety <: Variety
+The OSCAR type for abstract varieties is `AbstractVariety`.
 
 ## Constructors
 
@@ -60,7 +60,7 @@ degeneracy_locus(F::AbstractBundle, G::AbstractBundle, k::Int; class::Bool=false
 ```
 
 !!! note
-    Products and blowups are described elsewhere.
+    Products and blow-ups are described elsewhere.
 
 ## Underlying Data of an Abstract Variety
 
@@ -161,9 +161,9 @@ product(X::AbstractVariety, Y::AbstractVariety)
 ```
 
 !!! note
-    Blowups are described in their own section.
+    Blow-Ups are described in their own section.
 
-## Integrate Chow Ring Elements
+## Integrating Chow Ring Elements
 
 ```@julia
 integral(x::Union{MPolyDecRingElem, MPolyQuoRingElem})
@@ -187,7 +187,45 @@ AbstractBundle of rank 2 on AbstractVariety of dim 4
 julia> E = symmetric_power(Q, 3)
 AbstractBundle of rank 4 on AbstractVariety of dim 4
 
+julia> # Lines on a general cubic hypersurface in P^3:
+
 julia> integral(top_chern_class(E))
 27
 
 ```
+
+```jldoctest
+julia> T, (t, ) = polynomial_ring(QQ, [:t])
+(Multivariate polynomial ring in 1 variable over QQ, QQMPolyRingElem[t])
+
+julia> QT = fraction_field(T)
+Fraction field
+  of multivariate polynomial ring in 1 variable over QQ
+
+julia> P3 = abstract_projective_space(3, base = QT)
+AbstractVariety of dim 3
+
+julia> h = gens(P3)[1]
+h
+
+julia> integral(t^2*h^3+t*h)
+t^2
+
+```
+
+```jldoctest
+julia> G = abstract_grassmannian(2, 4+4)
+AbstractVariety of dim 12
+
+julia> S = tautological_bundles(G)[1]
+AbstractBundle of rank 2 on AbstractVariety of dim 12
+
+julia> E = symmetric_power(S, 2)
+AbstractBundle of rank 3 on AbstractVariety of dim 12
+
+julia> # Lines on a general complete intersection Calabi-Yau threefold of type (2,2,2,2):
+
+julia> integral(top_chern_class(E)^4)
+512
+
+```

experimental/IntersectionTheory/docs/src/AbstractVarietyMaps.md

@@ -5,6 +5,10 @@ DocTestSetup = Oscar.doctestsetup()
 
 # Abstract Variety Maps
 
+## Types
+
+The OSCAR type for abstract variety maps is `AbstractVarietyMap`.
+
 ## Constructors
 
 ```@docs

experimental/IntersectionTheory/docs/src/BlowUps.md

@@ -3,12 +3,12 @@ CurrentModule = Oscar
 DocTestSetup = Oscar.doctestsetup()
 ```
 
-# Blowups
+# Blow-Ups
 
 ```@docs
-blowup(i::AbstractVarietyMap; symbol::String = "e")
+blow_up(i::AbstractVarietyMap; symbol::String = "e")
 ```
 
 ```@docs
-blowup_points(X::AbstractVariety, n::Int; symbol::String = "e")
+blow_up_points(X::AbstractVariety, n::Int; symbol::String = "e")
 ```

experimental/IntersectionTheory/docs/src/BottFormulas.md

@@ -3,5 +3,78 @@ CurrentModule = Oscar
 DocTestSetup = Oscar.doctestsetup()
 ```
 
-# Bott Formulas
+# Bott's Formula
 
+## Abstract Varieties With a Torus Action
+
+### Types
+
+The OSCAR type for abstract varieties with a torus action is `TnVariety`.
+
+### Constructors
+
+```@docs
+tn_variety(n::Int, points::Vector{Pair{P, Int}}) where P
+```
+
+### Specialized Constructors
+
+```@docs
+tn_grassmannian(k::Int, n::Int; weights = :int)
+```
+
+```@docs
+tn_flag_variety(dims::Int...; weights = :int)
+```
+
+### Underlying Data of an Abstract Variety With a Torus Action
+
+
+```@docs
+dim(X::TnVariety)
+```
+
+```@docs
+fixed_points(X::TnVariety)
+```
+
+```@docs
+tangent_bundle(X::TnVariety)
+```
+
+```@docs
+tautological_bundles(X::TnVariety)
+```
+
+### Further Data Associated to an Abstract Variety With a Torus Action
+
+`trivial_line_bundle(X::TnVariety)`
+`cotangent_bundle(X::TnVariety)`
+`euler_number(X::TnVariety)`
+
+!!! note
+    If `X` is of type `TnVariety`, entering `total_chern_class(X)` returns the total Chern class of the tangent bundle of `X`.
+    Similarly for entering `chern_class(X, k)`.
+
+
+## Equivariant Abstract Bundles Under a Torus Action
+
+### Types
+
+### Constructors
+
+### Specialized Constructors
+
+### Underlying Data of an Equivariant Abstract Bundle
+
+### Further Data Associated to an Equivariant Abstract Bundle
+
+## Integrating ...
+
+
+
+## Example: Linear Subspaces on Hypersurfaces
+
+```@docs
+linear_subspaces_on_hypersurface(k::Int, d::Int; bott::Bool = true)
+```

experimental/IntersectionTheory/docs/src/examples.md

@@ -18,6 +18,7 @@ julia> integral(s1^4)
 2
 
 ```
+
 #### How Many Conics in $\mathbb P^3$ Meet Eight General Lines in $\mathbb P^3$?
 
 ```jldoctest
@@ -68,7 +69,7 @@ H
 julia> i = map(P2, P5, [2*h])
 AbstractVarietyMap from AbstractVariety of dim 2 to AbstractVariety of dim 5
 
-julia> Bl, E, j = blowup(i)
+julia> Bl, E, j = blow_up(i)
 (AbstractVariety of dim 5, AbstractVariety of dim 4, AbstractVarietyMap from AbstractVariety of dim 4 to AbstractVariety of dim 5)
 
 julia> e, HBl = gens(chow_ring(Bl))