| import OAI.NumberTheory.PiExponent.Ampleness.AdmissibleCurveModelDegrees | |
| namespace OAI | |
| noncomputable section | |
| namespace PiExponent.AdmissibleBlowupMargin | |
| open AlgebraicGeometry CategoryTheory TopologicalSpace | |
| open AdmissibleBlowupGeometry CurveNormalizationModel | |
| variable {ν Λ D : ℝ} (d : AdmissibleParameters ν Λ D) | |
| theorem affineCurveDegreeData (C : NumericalAmpleness.IntegralCurve (blowup d)) | |
| (hn : ¬ ∃ x : compactification d, Set.range (C.embedding ≫ projection d) ⊆ {x}) | |
| (hm : ∃ c : C.scheme, (C.embedding ≫ projection d) c ∈ (affineChart d).opensRange) : | |
| Nonempty (AffineCurveDegreeData d C) := by | |
| obtain ⟨r⟩ := AdmissibleCurveModel.existsModelData d C hn hm | |
| exact ⟨AdmissibleCurveModel.degreeData d C r⟩ | |
| end PiExponent.AdmissibleBlowupMargin | |
| namespace PiExponent.AdmissibleBlowupGeometry | |
| open AlgebraicGeometry | |
| variable {ν Λ D : ℝ} (d : AdmissibleParameters ν Λ D) | |
| theorem uniform_curve_margin : | |
| ∀ C : NumericalAmpleness.IntegralCurve (blowup d), | |
| uniformMargin d * (NumericalAmpleness.curveDegree (structureMap d) (H d) C : ℝ) ≤ | |
| (NumericalAmpleness.curveDegree (structureMap d) (interpolationBundle d) C : ℝ) := | |
| uniform_curve_margin_of_affine_curve_data d (AdmissibleBlowupMargin.affineCurveDegreeData d) | |
| end PiExponent.AdmissibleBlowupGeometry | |
| end | |
| end OAI | |