The local Rees Proj is a blow-up

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OAI.MaximalSeshadri.BlowupGluing.local_isBlowup

by wurtle · Nov 4, 2026 · Mathlib 0df444a (Lean v4.33.1)

maximal-seshadrioai-math

For a scheme $X$ , an ideal sheaf $I$ and an affine open $U$ , the Rees $\operatorname{Proj}$ chart with localProjection I U is a blow-up of localCentre I U.

Notation. IsBlowup I π says that $I$ pulls back to an invertible ideal along $\pi$ and that $\pi$ is universal with this property.

Formalization Note The statement is verbatim from OpenAI's Lean development, with Definitions files of this development imported in place of the upstream modules; these are supporting code for the statement.

Preamble

import Mathlib
import Definitions.Def_MaximalSeshadriConstants
import Definitions.Def_SeshadriPrelim6

namespace OAI

section
namespace MaximalSeshadri.BlowupGluing
noncomputable section
open CategoryTheory CategoryTheory.Limits AlgebraicGeometry
open MaximalSeshadri.Geometry

variable {X : Scheme.{0}} (I : X.IdealSheafData)

attribute [local instance] OAI.MaximalSeshadri.BlowupGluing.localAffine

Formal statement

theorem local_isBlowup (U : X.AffineZariskiSite) :
    IsBlowup (localCentre I U) (localProjection I U) := by
  sorry

end
end MaximalSeshadri.BlowupGluing
end
end OAI

Source

OpenAI, Maximal Seshadri constants on arbitrary polarized surfaces, September 23, 2026, https://github.com/openai/math (paper: preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf; Lean: lean/OAI/AlgebraicGeometry/Seshadri, Apache License 2.0); Lean declaration `OAI.MaximalSeshadri.BlowupGluing.local_isBlowup`, https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/AlgebraicGeometry/Seshadri/Blowup/Gluing.lean#L28

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