Instanton bundles on the Segre threefold with Picard number three

Abstract

We study instanton bundles $E$ on ${\mathbb{P}}^1\times {\mathbb{P}}^1\times {\mathbb{P}}^1$. We construct two different monads which are the analog of the monads for instanton bundles on ${\mathbb{P}}^3$ and on the flag threefold $F(0,1,2)$. We characterize the Gieseker semistable cases and we prove the existence of $\mu$-stable instanton bundles generically trivial on the lines for any possible $c_2(E)$. We also study the locus of jumping lines.

19 pages. Final version in Mathematische Nachrichten