In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically \(\theta \)-polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT.

中文翻译：

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颤动品种的辛分辨率

在本文中，我们从辛代数几何的角度考虑中岛箭袋的变种。我们证明它们都是在Beauville意义上的辛奇点，并且完全分类了允许辛解的类别。此外，我们证明了光滑轨迹与正典\（\ theta \）-多稳定点的轨迹重合，从而推广了Le Bruyn的结果。我们研究了它们的传说中的局部结构并找到了辛叶。我们的结果的一个有趣的结果是，并非所有颤动品种的辛辛苦解似乎都来自GIT的变化。