论文标题
$ \ mathbb {z}/k \ mathbb {z} $ - $ \ mathbb {a}^2 $的模量空间
Moduli spaces of $\mathbb{Z}/k\mathbb{Z}$-constellations over $\mathbb{A}^2$
论文作者
论文摘要
令$ρ：\ mathbb {z}/k \ mathbb {z} \ rightarrow \ text {sl}（2，2，\ mathbb {c}）$是有限的阿贝尔组的表示，让$θ^{\ text^{\ text {gen}} {gen}} \ subset} \ subset \ subset \ subset \ subset { \ text {hom} _ \ mathbb {z}（r（\ mathbb {z}/k \ mathbb {z}），\ mathbb {q}）$是$ g $ stellations的集合。我们提供了所有Chambers $ C \subsetθ^{\ text {gen}} $的组合描述，并证明其中有$ k！$。此外，我们介绍了简单室的概念，我们表明，为了了解所有感谢您的$ g $ stellations，就足以构建所有简单的会议室。我们还证明有$ k \ cdot 2^{k-2} $简单的钱伯斯。 Finally, we provide an explicit formula for the tautological bundles $\mathscr{R}_C$ over the moduli spaces $\mathscr{M} _C$ for all chambers $C\subset Θ^{\text{gen}}$ which only depends upon the chamber stair which is a combinatorial object attached to the chamber $C$.
Let $ρ:\mathbb{Z}/k \mathbb{Z}\rightarrow \text{SL}(2,\mathbb{C})$ be a representation of a finite abelian group and let $Θ^{\text{gen}}\subset \text{Hom}_\mathbb{Z}(R(\mathbb{Z}/k\mathbb{Z}),\mathbb{Q})$ be the space of generic stability conditions on the set of $G$-constellations. We provide a combinatorial description of all the chambers $C\subsetΘ^{\text{gen}}$ 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\cdot 2^{k-2} $ simple chambers. Finally, we provide an explicit formula for the tautological bundles $\mathscr{R}_C$ over the moduli spaces $\mathscr{M} _C$ for all chambers $C\subset Θ^{\text{gen}}$ which only depends upon the chamber stair which is a combinatorial object attached to the chamber $C$.
