Cokernel bundles and Fibonacci bundles

Details Cokernel bundles and Fibonacci bundles Cokernel bundles and Fibonacci bundles

2005-05-13

arxiv.org/abs/math/0505290v2

Mathematische Nachrichten, 281 (2008), n. 4, 1-18

Mathematics

Algebraic Geometry

23 pages, 1 figure, revised version, to appear in Mathematische Nachrichten

Scientific paper

We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a resolution of the form $$ 0 \to \mathbb{C}^s \otimes E \xrightarrow{\mu} \mathbb{C}^t \otimes F \to C \to 0.$$ 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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