Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd rank that they are birational to Hilbert schemes. The argument makes use of a new Chow-theoretic result, showing that moduli spaces on an Enriques surface give rise to constant cycle subvarieties of the moduli spaces of the covering K3.

中文翻译：

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Enriques曲面上稳定物体的模空间的双几何

使用K3曲面的墙交叉，我们针对不同的稳定性条件，在通用Enriques曲面上建立了稳定对象的模空间的双等式。作为一个应用，我们证明了在奇数秩的Mukai向量的情况下，它们对希尔伯特方案是双理性的。该论点利用了新的Chow-理论结果，表明Enriques曲面上的模空间产生了覆盖K3的模空间的恒定循环子变量。