## Tohoku Mathematical Journal 2014 September SECOND SERIES VOL. 66, NO. 3

 Tohoku Math. J. 66 (2014), 355-375

Title DANILOV'S RESOLUTION AND REPRESENTATIONS OF THE MCKAY QUIVER

Author Oskar Kędzierski

(Received January 11, 2011, revised June 21, 2013)
Abstract. We construct a family of McKay quiver representations on the Danilov resolution of the $\frac{1}{r}(1,a,r-a)$ singularity. This allows us to show that the resolution is the normalization of the coherent component of the fine moduli space of $\theta$-stable McKay quiver representations for a suitable stability condition $\theta$. We describe explicitly the corresponding union of chambers of stability conditions for any coprime numbers $r,a$.

Mathematics Subject Classification. Primary 14E16; Secondary 16G20, 14L24.

Key words and phrases. McKay correspondence, resolutions of terminal quotient singularities, Danilov resolution, moduli of quiver representations.

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