Simplicity of generic Steiner bundles

Brambilla, Maria Chiara

Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 723-735

Résumé

A Steiner bundle $E$ on $\mathbb{P}^{n}$ has a linear resolution of the form $0 \rightarrow \mathcal{O}(-1)^{s}\rightarrow \mathcal{O}^{t}\rightarrow E \rightarrow 0$. In this paper we prove that a generic Steiner bundle $E$ is simple if and only if $\chi (\mathrm{End} E)$ is less or equal to 1. In particular we show that either $E$ is exceptional or it satisfies the inequality $t\leq \left( \frac{n+1+\sqrt{(n+1)^{2}-4}}{2} \right)s$.