Year: 2024
Type: preprint
Abstract: In this paper, we study in detail the hyperbolic covers $\tilde{W}$ and $\hat{W}$ of an elliptic Weyl system introduced by Saito. We show that they are isomorphic and also isomorphic to an extended Coxeter system of star type. For $\tilde{c}$ a Coxeter transformation in $\tilde{W}$ we can conclude the Hurwitz transitivity of the braid group action on the set of reduced reflection factorizations of $\tilde{c}$ from the Hurwitz transitivity in extended Coxeter systems of star type. This then enables us to establish for a weighted projective line $\mathbb{X}$ of tubular type an order preserving bijection between the poset of thick subcategories of $\mathrm{coh}(\mathbb{X})$ generated by an exceptional sequence and the poset $[\mathrm{id}, \tilde{c}]$ ordered by the absolute order. In an Appendix, we study the hyperbolic cover of a Coxeter system.
Source: arXiv (Cornell University)
Authors: Baumeister, Barbara, Wegener, Patrick
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404401701