Even and odd instanton bundles on Fano threefolds

Abstract

We define non-ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) instanton bundles. We determine a lower bound for the quantum number of a non-ordinary instanton bundle, i.e. the degree of its second Chern class, showing the existence of such bundles for each admissible value of the quantum number when $i_X\ge 2$ or $i_X=1$, $\mathrm{Pic}(X)$ is cyclic and $X$ is ordinary. In these cases we deal with the component inside the moduli spaces of simple bundles containing the vector bundles we construct and we study their restriction to lines. Finally we give a monadic description of non-ordinary instanton bundles on ${\mathbb{P}}^3$ and the smooth quadric studying their loci of jumping lines, when of the expected codimension.

arXiv comment34 pages. Minor changes. The final version will appear in The Asian Journal of Mathematics

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Cited by in corpus (3)

• Instantons: the next frontier
• Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1
• $\ell$-away ACM Bundles on Fano Surfaces