Moduli spaces of ℤ/kℤ-constellations over 𝔸2

Let Formula: see text be a representation of a finite abelian group and let Formula: see text be the space of generic stability conditions on the set of Formula: see text-constellations. We provide a combinatorial description of all the chambers Formula: see text and prove that there are Formula: see text of them. Moreover, we introduce the notion of simple chamber and we show that, in order to know all toric Formula: see text-constellations, it is enough to build all simple chambers. We also prove that there are Formula: see text simple chambers. Finally, we provide an explicit formula for the tautological bundles Formula: see text over the moduli spaces Formula: see text for all chambers Formula: see text which only depends upon the chamber stair which is a combinatorial object attached to the chamber Formula: see text.