Let rho : Z/kZ -> SL(2, Z) be a representation of a finite abelian group and let Theta(gen) subset of Hom Z(R(Z/kZ), Q) be the space of generic stability conditions on the set of G-constellations. We provide a combinatorial description of all the chambers C subset of Theta(gen) and prove that there are k of them. Moreover, we introduce the notion of simple chamber and we show that, in order to know all toric G-constellations, it is enough to build all simple chambers. We also prove that there are k center dot 2(k-2) simple chambers. Finally, we provide an explicit formula for the tautological bundles R-C over the moduli spaces R-C for all chambers C subset of Theta(gen) which only depends upon the chamber stair which is a combinatorial object attached to the chamber C.
