Connectedness and normality conjecture for finite-type quiver varieties

Fix a quiver of finite type, take $m=(1,\dots,1)$ and $\lambda=0$, and let $d,v$ be fixed. Write $M_{m,0}(d,v)$ and $M_{0,0}(d,v)$ for the corresponding quiver varieties. Connectedness and normality conjecture. The variety $M_{m,0}(d,v)$ is connected, and the variety $M_{0,0}(d,v)$ is normal. This is the conjecture proposed for finite-type quiver varieties after reducing to the case $v_i>0$ for all vertices. The supplied text does not indicate whether it has been resolved.