We define non--ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) instanton bundles introduced in \cite{C--C--G--M}. 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 $i_X=1$, $\rk \Pic(X)=1$ 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 $\p3$ and the smooth quadric studying their loci of jumping lines, when of the expected codimension.

Even and odd instanton bundles on Fano threefolds / Antonelli, Vincenzo; Casnati, Gianfranco; Genc, Ozhan. - In: THE ASIAN JOURNAL OF MATHEMATICS. - ISSN 1093-6106. - STAMPA. - 26:1(2022), pp. 081-118.

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 introduced in \cite{C--C--G--M}. 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 $i_X=1$, $\rk \Pic(X)=1$ 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 $\p3$ and the smooth quadric studying their loci of jumping lines, when of the expected codimension.
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2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2975418