---
_id: '63620'
abstract:
- lang: eng
  text: We introduce a new class of reflection groups associated with the canonical
    bilinear lattices of Lenzing, which we call reflection groups of canonical type.
    The main result of this work is a categorification of the corresponding poset
    of non-crossing partitions for any such group, realized via the poset of thick
    subcategories of the category of coherent sheaves on an exceptional hereditary
    curve generated by an exceptional sequence. A second principal result, essential
    for the categorification, is a proof of the transitivity of the Hurwitz action
    in these reflection groups.
author:
- first_name: Barbara
  full_name: Baumeister, Barbara
  last_name: Baumeister
- first_name: Igor
  full_name: Burban, Igor
  id: '72064'
  last_name: Burban
- first_name: Georges
  full_name: Neaime, Georges
  last_name: Neaime
- first_name: Charly Merlin
  full_name: Schwabe, Charly Merlin
  id: '103440'
  last_name: Schwabe
citation:
  ama: Baumeister B, Burban I, Neaime G, Schwabe CM. Non-crossing partitions for exceptional
    hereditary curves. <i>arXiv:251201729</i>. Published online 2025.
  apa: Baumeister, B., Burban, I., Neaime, G., &#38; Schwabe, C. M. (2025). Non-crossing
    partitions for exceptional hereditary curves. In <i>arXiv:2512.01729</i>.
  bibtex: '@article{Baumeister_Burban_Neaime_Schwabe_2025, title={Non-crossing partitions
    for exceptional hereditary curves}, journal={arXiv:2512.01729}, author={Baumeister,
    Barbara and Burban, Igor and Neaime, Georges and Schwabe, Charly Merlin}, year={2025}
    }'
  chicago: Baumeister, Barbara, Igor Burban, Georges Neaime, and Charly Merlin Schwabe.
    “Non-Crossing Partitions for Exceptional Hereditary Curves.” <i>ArXiv:2512.01729</i>,
    2025.
  ieee: B. Baumeister, I. Burban, G. Neaime, and C. M. Schwabe, “Non-crossing partitions
    for exceptional hereditary curves,” <i>arXiv:2512.01729</i>. 2025.
  mla: Baumeister, Barbara, et al. “Non-Crossing Partitions for Exceptional Hereditary
    Curves.” <i>ArXiv:2512.01729</i>, 2025.
  short: B. Baumeister, I. Burban, G. Neaime, C.M. Schwabe, ArXiv:2512.01729 (2025).
date_created: 2026-01-15T09:37:34Z
date_updated: 2026-07-06T07:56:11Z
external_id:
  arxiv:
  - '2512.01729'
language:
- iso: eng
publication: arXiv:2512.01729
status: public
title: Non-crossing partitions for exceptional hereditary curves
type: preprint
user_id: '103440'
year: '2025'
...