DANILOV'S RESOLUTION AND REPRESENTATIONS OF THE MCKAY QUIVER

摘要

We construct a family of McKay quiver representations on the Danilov resolution of the 1/r (1, a, r - a) singularity. This allows us to show that the resolution is the normalization of the coherent component of the fine moduli space of θ-stable McKay quiver representations for a suitable stability condition θ. We describe explicitly the corresponding union of chambers of stability conditions for any coprime numbers r, a.