Even and odd instanton bundles on Fano threefolds (Q2689084)

The authors go beyond the already widely studied notion of ordinary instanton bundles usually referred to as instanton bundles. They studied non-ordinary instanton vector bundles giving their properties and constructed some examples on Fano threefolds. They determined lower bounds for the quantum number of a non-ordinary bundle \(\mathscr{E}\) that is the degree of \(c_2(\mathscr{E})\) essentially showing the existence of such bundles for each admissible value of the quantum number where the index of \(X\), \(i_X\geq2\) or \(i_X=1\) and the Picard number of \(X\) is one. Finally they gave a monadic description of non-ordinary instanton bundles on \(\mathbb{P}^3\) and \(Q\). That is they proved the existence of monads for the non-ordinary instanton bundles when \(X\) is either the projective space \(\mathbb{P}^3\) or the smooth quadric \(Q\).