论文标题
CDV奇点的BPS不变性的消失和对称性
Vanishing and Symmetries of BPS Invariants for CDV Singularities
论文作者
论文摘要
本文表明，与复合du-val奇异性的非交换性毛虫分辨率相关的动机BP不变性由Iyama-Wemyss的作品中出现的标记的Dynkin Combinatorics控制。特别是，我们表明，不变的尺寸向量消失了，而尺寸向量并不是从天然商图下从仿射根系中获得的限制根的倍数。直接的推论是对曲线类别的描述，即几何毛虫分辨率的gopakumar-vafa不变式消失，从而将nabijou的最新结果概括为wemyss- wemysss to nocorated设置。我们还制定了一种使用派生的等效性在非逐渐变化的不变式之间查找对称性的方法，并显示如何将其应用于某些设置中的线束曲折和突变函数。特别是，我们发现CDV奇点的不同毛虫分辨率的gopakumar-vafa不变性之间的新墙壁横断关系。
This paper shows that the motivic BPS invariants associated to a noncommutative crepant resolution of a compound Du-Val singularity are controlled by the labelled Dynkin combinatorics appearing in the work of Iyama--Wemyss. In particular, we show that the invariants vanish for dimension vectors which are not a multiple of a restricted root obtained from the affine root system under a natural quotient map. An immediate corollary is a description of the curve classes for which the Gopakumar--Vafa invariants of geometric crepant resolutions vanish, generalising a recent result of Nabijou--Wemyss to the nonisolated setting. We furthermore formulate a method for finding symmetries among the non-vanishing invariants using derived equivalences, and show how this can be applied to line bundle twists and mutation functors in some settings. In particular, we find new wall-crossing relations among the Gopakumar-Vafa invariants of the different crepant resolutions of a cDV singularity.
