Twisted ideal power inclusions are monomorphisms

Proved

OAI.MaximalSeshadri.Geometry.twistedIdealPowerInclusion_mono

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

maximal-seshadrioai-math

For line bundles $L,J$ on a scheme, a monomorphism $\iota:J\to\mathcal O_X$ , and $a,b,n$ : the map $(L^a\otimes J^b)^n\to L^{an}$ (twistedIdealPowerInclusion) is a monomorphism.

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.Geometry
noncomputable section
open AlgebraicGeometry CategoryTheory TopologicalSpace
open MaximalSeshadri.Frames

variable {X : Scheme.{0}}

Formal statement

theorem twistedIdealPowerInclusion_mono (L J : LineBundle X) (ι : J.sheaf ⟶ O X)
    [Mono ι] (a b n : ℕ) : Mono (twistedIdealPowerInclusion L J ι a b n) := by
  sorry

end
end MaximalSeshadri.Geometry
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.Geometry.twistedIdealPowerInclusion_mono`, https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/AlgebraicGeometry/Seshadri/LocalAlgebra/TwistedIdealPower.lean#L32

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