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arXiv · 1505.02103

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

Yum-Tong Siu
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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.

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Yum-Tong Siu. 2015-05-08. Splitting of unstable 2-bundles over the complex projective 6-space. https://arxiv.org/abs/1505.02103

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