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arXiv · 2207.14120

Relations among $\mathbb{P}$-Twists

Andreas Hochenegger·Andreas Krug
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Abstract

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 hyperk\"ahler 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.

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Andreas Hochenegger, Andreas Krug. 2022-07-28. Relations among $\mathbb{P}$-Twists. https://doi.org/10.1093/imrn%2Frnaf056

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