| import OAI.NumberTheory.PiExponent.Ampleness.AdmissibleJetAmpleness |
| import OAI.NumberTheory.PiExponent.Ampleness.BlowupJetSurjectivityComplete |
|
|
| namespace OAI |
|
|
| namespace PiExponent.AdmissibleJetSurjectivity |
| noncomputable section |
| open AlgebraicGeometry CategoryTheory TopologicalSpace |
| open PiExponentSeshadri.Geometry |
| open PiExponent.AdmissibleBlowupGeometry PiExponent.BlowupJetSurjectivity |
| attribute [local irreducible] AdmissibleBlowupGeometry.centerIdeal |
| AdmissibleBlowupGeometry.hyperplane |
| variable {ν Λ D : ℝ} (d : AdmissibleParameters ν Λ D) |
|
|
| theorem eventual_jetRestriction_surjective : |
| ∃ N, ∀ n, N ≤ n → Function.Surjective |
| (jetRestriction (centerIdeal d) (hyperplane d) n) := by |
| exact eventual_blowup_jetRestriction_surjective |
| (compactificationStructureMap d) (centerIdeal d) (hyperplane d) (blowupBundle_ample d) |
|
|
| theorem eventually_jetRestriction_surjective : |
| ∀ᶠ n in Filter.atTop, Function.Surjective |
| (jetRestriction (centerIdeal d) (hyperplane d) n) := by |
| obtain ⟨N,hN⟩ := eventual_jetRestriction_surjective d |
| exact Filter.eventually_atTop.mpr ⟨N,hN⟩ |
|
|
| end |
| end PiExponent.AdmissibleJetSurjectivity |
|
|
| end OAI |
|
|
