/-
Copyright 2025 The Formal Conjectures Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-/
module
public import Mathlib.AlgebraicGeometry.Limits
public import Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
public import Mathlib.RingTheory.MvPolynomial.Homogeneous@[expose] public section-- The contents of this file will be in mathlib as of #26061
universe u vopen CategoryTheory Limits MvPolynomial AlgebraicGeometryvariable (n : Type v) (S : Scheme.{max u v})local notation "ℤ[" n "]" => homogeneousSubmodule n ℤlocal notation3 "ℤ[" n "].{" u "," v "}" => homogeneousSubmodule n (ULift.{max u v} ℤ)attribute [local instance] MvPolynomial.gradedAlgebra
The projective space over a scheme S, with homogeneous coordinates indexed by n
noncomputable def ProjectiveSpace : Scheme.{max u v} :=
pullback (terminal.from S) (terminal.from (Proj ℤ[n].{u, v}))
ℙ(n; S) is the affine S indexed by n
scoped [AlgebraicGeometry] notation "ℙ("n"; "S")" => ProjectiveSpace n S