论文标题
$ \ mathbb {p} $ - 曲折之间的关系
Relations among $\mathbb{P}$-Twists
论文作者
论文摘要
给定了两个代数三角类别中的两个$ \ mathbb {p} $ - 对象，我们调查了相关的$ \ mathbb {p} $ - twists之间的可能关系。主要结果是，在某些技术假设下，$ \ mathbb {p} $ - twists ting coldute且仅当$ \ mathbb {p} $ - 对象是正交的。否则，根本没有关系。特别是，这适用于$ \ mathbb {p} $ - Hyperkähler品种上的对象。为了证明这一点，我们将$ \ mathbb {p} $ - 曲折联系起来，以获取球形曲折，并采用已知结果，以了解两对球形曲折之间没有关系的结果。
Given two $\mathbb{P}$-objects in some algebraic triangulated category, we investigate the possible relations among the associated $\mathbb{P}$-twists. The main result is that, under certain technical assumptions, the $\mathbb{P}$-twists commute if and only if the $\mathbb{P}$-objects are orthogonal. Otherwise, there are no relations at all. In particular, this applies to most of the known pairs of $\mathbb{P}$-objects on hyperkähler varieties. In order to show this, we relate $\mathbb{P}$-twists to spherical twists and apply known results about the absence of relations between pairs of spherical twists.
