| 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 |
|
|
