| import Mathlib |
| import OAI.AlgebraicGeometry.Seshadri.Projective.ProjectiveCartier |
| import OAI.AlgebraicGeometry.Seshadri.Intersection.FiniteLineEuler |
| import OAI.AlgebraicGeometry.Seshadri.Nodal.NodalDivisorDegree |
| import OAI.AlgebraicGeometry.Seshadri.Nodal.NodalIdealEuler |
| import OAI.AlgebraicGeometry.Seshadri.Projective.QuarticDivision |
| import OAI.AlgebraicGeometry.Seshadri.Intersection.CurveSectionDegree |
| import OAI.AlgebraicGeometry.Seshadri.Sheaves.ClosedPushforwardExact |
| import OAI.AlgebraicGeometry.Seshadri.Cohomology.CycleStructures |
| import OAI.AlgebraicGeometry.Seshadri.Intersection.ArbitraryCartierEuler |
| import OAI.AlgebraicGeometry.Seshadri.Sheaves.BaseChangeNatural |
| import OAI.AlgebraicGeometry.Seshadri.Interpolation.SurfaceQuadrilateral |
| import OAI.AlgebraicGeometry.Seshadri.Geometry.AmplePowers |
| import OAI.AlgebraicGeometry.Seshadri.Blowup.BoundaryNef |
| import OAI.AlgebraicGeometry.Seshadri.Interpolation.SeshadriUpper |
|
|
| namespace OAI |
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| |
| section |
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| namespace MaximalSeshadri.Geometry |
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| theorem maximalSeshadriConstants (S : Surface) (L : LineBundle S.scheme) |
| (hL : LineBundle.IsAmple S.scheme L) : EventualMaximalSeshadri S L := by |
| obtain ⟨r₀,hr₀,h⟩ := S.eventual_very_general_curve_lower L hL |
| refine ⟨r₀,hr₀,fun r hr => ?_⟩ |
| obtain ⟨Z,hZ,hne,hC⟩ := h r hr |
| refine ⟨Z,hZ,hne,fun p hp => ?_⟩ |
| have hrpos : 0 < r := hr₀.trans_le hr |
| obtain ⟨B⟩ := S.pointBlowup_exists L hL r p |
| exact ⟨⟨B,B.boundaryNef_of_curve_bound S L hL hrpos (hC p hp)⟩, |
| S.seshadri_eq_of_curve_lower L hL hrpos p (hC p hp)⟩ |
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| end MaximalSeshadri.Geometry |
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| end |
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| end OAI |
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