Weight Spaces and Attracting Sets for Torus Actions on Quiver Moduli

We study torus actions on moduli spaces of quivers. First we give a description of the weight spaces of the induced action of the tangent space to a torus-fixed point. Then we focus on actions of tori of rank one and derive an explicit form for the attractors in the Bia{\l}ynicki-Birula decomposition.