论文标题
类型$ \ mathbb {a} $ Quivers的总稳定性功能
Total stability functions for type $\mathbb{A}$ quivers
论文作者
论文摘要
对于Dynkin类型$ \ Mathbb {a} _n $的颤抖$ q $，我们给出了一组$ n-1 $的不平等现象，对于线性稳定性条件（又称中央费用）$ z \ z \ colon k_0（q）\ to \ mathbb {c} $，使所有不可或缺的代表性都可以使所有不可或缺的代表均匀。我们还表明，这些是一组最小的不平等集合，定义了总稳定性条件的空间$ \ mathcal {ts}（q）$，被认为是$ \ m athbb {r}^{q_0}^{q_0} \ times（\ mathbb {\ mathb {r} _ {r} _ {> 0} _ {> 0}____________________________________________________________________________________________________________________。然后，我们使用这些不等式表明，$ \ Mathcal {ts}（q）$的预测的每纤维to $（\ Mathbb {r} _ {> 0}）^{q_0} $是线性的，等于$ \ \ m}
For a quiver $Q$ of Dynkin type $\mathbb{A}_n$, we give a set of $n-1$ inequalities which are necessary and sufficient for a linear stability condition (a.k.a. central charge) $Z\colon K_0(Q) \to \mathbb{C}$ to make all indecomposable representations stable. We furthermore show that these are a minimal set of inequalities defining the space $\mathcal{TS}(Q)$ of total stability conditions, considered as an open subset of $\mathbb{R}^{Q_0} \times (\mathbb{R}_{>0})^{Q_0}$. We then use these inequalities to show that each fiber of the projection of $\mathcal{TS}(Q)$ to $(\mathbb{R}_{>0})^{Q_0}$ is linearly equivalent to $\mathbb{R} \times \mathbb{R}_{>0}^{Q_1}$.
