Merge pull request #22 from StardustMath/Durham_2024

Add functionality for canonical divisor.

experimental/Durham2024/src/fixes.jl

@@ -16,3 +16,12 @@ function getindex(D::AbsAlgebraicCycle, C::AbsAlgebraicCycle)
   return D[first(comps)]
 end
 
+function canonical_divisor(X:: AbsAffineScheme{<:Field, <:MPolyRing}) 
+  return CartierDivisor(covered_scheme(X), ZZ)
+end
+
+
+
+
+
+

experimental/Durham2024/test/runtests2.jl

@@ -0,0 +1,34 @@
+@testset "canonical divisor of a Kleinian singularity" begin
+# We calculate the canonical divisor of the blow up of a Kleinian singularity in this document.
+R, (x, y, z) = QQ[:x, :y, :z] 
+I = ideal(R, [x^3 - y*z])  
+
+IA3 = spec(R)
+X, inc_X = sub(IA3, I) #X is the A2 Kleinian singularity
+I_sing = ideal(R, gens(R))
+
+pr1 = blow_up(IA3, I_sing) #blow up the affine space IA3
+bl_IA3 = domain(pr1) 
+E = exceptional_divisor(pr1) 
+bl_X, inc_bl_X, pr2 = strict_transform(pr1, inc_X) #bl_X is the blow up of X
+
+#the canonical divisor of bl_IA3
+bl_IA3_canonical_divisor = pullback(pr1, Oscar.canonical_divisor(IA3)) + (dim(IA3)-1)*E
+
+# the cartier divisor of IA3 that correspdonds to X
+X_ideal = image_ideal(inc_X)
+X_ideal_sheaf = ideal_sheaf(codomain(pr1),  IA3, X_ideal)
+X_divisor = EffectiveCartierDivisor(X_ideal_sheaf)
+
+#the cartier divisor of bl_IA3 that correspdonds to bl_X
+bl_X_divisor = strict_transform(pr1, X_divisor) 
+
+# the canonical divisor of bl_X
+bl_X_canonical_divisor = pullback(inc_bl_X, bl_IA3_canonical_divisor + bl_X_divisor)
+end
+
+
+
+
+
+