harthshorne_conjecture

Specification

There are no indecomposable vector bundles of rank 2 on $\mathbb{P}^n$ for $n \ge 7$. This is conjecture 6.3 in _VARIETIES OF SMALL CODIMENSION IN PROJECTIVE SPACE_, R. Hartshorne

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Lean 4 Statement

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))

ID: Paper__HartshorneConjecture__harthshorne_conjecture

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