Cokernel bundles and Fibonacci bundles

We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a resolution of the form $0 \to \mathbb{C}^s \otimes E \xrightarrowμ \mathbb{C}^t \otimes F \to C \to 0.$ In this paper we prove that, under suitable conditions on $(E,F)$, a generic bundle with this form is either simple or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on $\mathbb{P}^2$ and we prove the stability when $E = \mathcal{O}$, $F = \mathcal{O}(1)$ and $C$ is an exceptional bundle on $\mathbb{P}^N$ for $N \geq 2$.

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