A direct proof that toric rank $2$ bundles on projective space split


  • David Stapleton




The point of this paper is to give a short, direct proof that rank $2$ toric vector bundles on $n$-dimensional projective space split once $n$ is at least $3$. This result is originally due to Bertin and Elencwajg, and there is also related work by Kaneyama, Klyachko, and Ilten-Süss. The idea is that, after possibly twisting the vector bundle, there is a section which is a complete intersection.


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How to Cite

Stapleton, D. (2020). A direct proof that toric rank $2$ bundles on projective space split. MATHEMATICA SCANDINAVICA, 126(3), 493–496. https://doi.org/10.7146/math.scand.a-121452