Dynkin Quivers 的完整异常集合和稳定性条件

Pub Date : 2024-05-27 DOI:10.1093/imrn/rnae110

Takumi Otani

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引用次数: 0

摘要

对于三角范畴上的稳定条件 $\sigma $，季米特洛夫-卡扎科夫引入了 $\sigma $- 异常集合的概念。在本文中，我们将研究无环簇的派生类中的全（$\sigma $）例外集合。特别是，我们证明了在Dynkin quiver的派生类中，任何稳定条件$\sigma $都包含一个完整的$\sigma $-异常集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Full Exceptional Collections and Stability Conditions for Dynkin Quivers

For a stability condition $\sigma $ on a triangulated category, Dimitrov–Katzarkov introduced the notion of a $\sigma $-exceptional collection. In this paper, we study full $\sigma $-exceptional collections in the derived category of an acyclic quiver. In particular, we prove that any stability condition $\sigma $ on the derived category of a Dynkin quiver admits a full $\sigma $-exceptional collection.

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