Moduli spaces of ℤ/kℤ-constellations over 𝔸2
Michele Graffeo
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Source: Crossref
Published: Jun 26, 2024
DOI: 10.1142/s0219199724500196
Open original source ↗Source abstract
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].
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