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arXiv · 2311.17762

Exchange graphs and Ext-quivers of hearts of tube categories

Mingfa Chen
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Abstract

In this paper we introduce the notion of pre-simple-minded collection (pre-SMC) of type $\mathbb{A}$ in the bounded derived categories $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$ of tube categories $\textbf{T}_{p}$ of rank $p$. This provides an effective approach to classify the hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$. We then use this classification to prove the exchange graph of hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$ is connnected. Further, we classify the Ext-quivers of hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$. As an application, we show that the space of Bridgeland stability conditions on $\mathcal{D}^{b}(${\rm{\textbf{T}}}$_p)$ is connected.

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Mingfa Chen. 2023-11-29. Exchange graphs and Ext-quivers of hearts of tube categories. https://arxiv.org/abs/2311.17762

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