Splitting of unstable 2-bundles over the complex projective 6-space

TL;DR

This paper proves that any unstable holomorphic 2-bundle over complex projective space of dimension at least 6 must split into line bundles, resolving a long-standing conjecture for dimensions n ≥ 4.

Contribution

It establishes the splitting of unstable 2-bundles over complex projective spaces of dimension n ≥ 6, extending previous results and using advanced geometric theorems.

Findings

Unstable 2-bundles split into line bundles for n ≥ 6.

Resolved the conjecture for n ≥ 4.

Applied Peternell's singular variety version of Barth-Lefschetz theorem.

Abstract

We prove that any unstable holomorphic 2-bundle over the complex projective space of complex dimension n at least 6 must split into a direct sum of two holomorphic line bundles. The statement with the weaker dimension condition of n at least 4 has been an open conjecture since 1977. One ingredient in our method uses Mathias Peternell's singular variety version of the Barth-Lefschetz theorem which requires the strong dimension condition of n at least 6.