Relations Among ℙ-Twists
Year: 2025
Type: article
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 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.
DOI: 10.1093/imrn/rnaf056
Authors: Andreas Hochenegger, Andreas Krug
Institutions: Politecnico di Milano, Leibniz University Hannover
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,534
OpenAlex ID: W4409104613