We define non–ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) instanton bundles introduced in [14]. 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 $i_X \geq 2$ or $i_X = 1$ and $\mathrm{rk} \: \operatorname{Pic}(X) = 1$. 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.

中文翻译：

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Fano 三重折叠上的偶数和奇数瞬子束

我们在 Fano 三重 $X$ 上定义了非普通的瞬子束，扩展了 [ 14 ] 中引入的（普通）瞬子束的概念。我们确定非普通瞬子束的量子数的下限，即其第二陈类的度数，表明当 $i_X \geq 2$ 或 $i_X 时，对于每个允许的量子数值都存在此类束= 1$ 和 $\mathrm{rk} \: \operatorname{Pic}(X) = 1$。在这些情况下，我们处理包含我们构造的向量丛的单丛模空间内的分量，并研究它们对线的限制。最后，我们给出了 $\mathbb{P}^3$ 上的非普通瞬子束的单子描述，以及研究它们的跳跃线轨迹的平滑二次曲面，以及预期的余维。