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7f5fab8 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | import Mathlib
import OAI.AlgebraicGeometry.Seshadri.Model
namespace OAI
namespace MaximalSeshadri.Geometry
noncomputable section
open CategoryTheory AlgebraicGeometry TopologicalSpace
open scoped AlgebraicGeometry
variable {X : Scheme.{0}}
abbrev complexSectionModule (f : X ⟶ Spec (CommRingCat.of ℂ)) (M : X.Modules) :
Module ℂ (GlobalSections X M) :=
Module.compHom _ (baseScalars f)
end
end MaximalSeshadri.Geometry
namespace MaximalSeshadri.Geometry
noncomputable section
open CategoryTheory CategoryTheory.Limits AlgebraicGeometry TopologicalSpace
open scoped AlgebraicGeometry
def EventualSeshadriEquality (S : Surface) (L : LineBundle S.scheme) : Prop :=
∃ r₀ : ℕ, 0 < r₀ ∧ ∀ r : ℕ, r₀ ≤ r →
∃ Z : ℕ → Set (Configuration S r),
(∀ n, IsClosed (Z n) ∧ Z n ≠ Set.univ) ∧
(∃ p : Configuration S r, ∀ n, p ∉ Z n) ∧
∀ p : Configuration S r, (∀ n, p ∉ Z n) →
seshadriConstant S L r p = Real.sqrt ((selfIntersection S L : ℝ) / r)
end
end MaximalSeshadri.Geometry
end OAI
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