Source labels openChecked July 26, 2026

Hartshorne Conjecture

There are no indecomposable vector bundles of rank 2 on $\mathbb{P}^n$ for $n \ge 7$ . This is Conjecture 6.3 in [Har1974].

Algebraic geometry AMS 14

Mathematical statement

There are no indecomposable vector bundles of rank 2 on $\mathbb{P}^n$ for $n \ge 7$ . This is Conjecture 6.3 in [Har1974].

Statement source: Papers statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

harthshorne_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem harthshorne_conjecture (n : ℕ) (hn : 7 ≤ n)    (𝓕 : VectorBundles ℙ(Fin (n + 1); Spec (.of ℂ)))    (h𝓕 : 𝓕.rank = 2) :    Nonempty (𝓕.Splitting (Fin 2)) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Varieties of small codimension in projective spacebackground Evidences on Hartshorne's conjecture? References?background