Smooth correspondences between quiver varieties

We introduce a new class of smooth correspondences between Nakajima quiver varieties called split parabolic quiver varieties, and study their properties. We use these correspondences to construct an explicit resolution of singularities of quiver Brill–Noether loci and prove that the latter are irreducible and Cohen-Macaulay of expected dimension (if non-empty). This generalizes the results of Nakajima–Yoshioka and Bayer–Chen–Jiang for Hilbert schemes of points on surfaces.

💡 Research Summary

The paper introduces a new class of smooth correspondences between Nakajima quiver varieties, called split parabolic quiver varieties, and uses them to study the geometry of quiver Brill–Noether loci.

After recalling the construction of Nakajima quiver varieties (M_Q(\mathbf d;\mathbf f)) as GIT quotients of the zero‑level of the moment map on the representation space of the doubled framed quiver, the authors define split parabolic quiver varieties (M_Q