Uniform vector bundles on a projective space
Uniform vector bundles on a projective space
It is well known [1] that a vector bundle $E$ on $P^{1}$ is isomorphic to a direct sum of line bundles $O_{P^{1}}(a_{1})\oplus\cdots\oplus O_{P^{1}}(a_{p})$ where $a_{1},$ $\cdots$ , $a_{p}(a_{1}\geqq\cdots\geqq a_{p})$ are uniquely determined, and we say that $E$ is of type $(a_{1}, \cdots , a_{p})$ .Then according to Schwarzenberger, we have …