Non-crossing partitions for exceptional hereditary curves
Representation Theory
2025-12-02 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.2512.01729,
title = {Non-crossing partitions for exceptional hereditary curves},
author = {Barbara Baumeister and Igor Burban and Georges Neaime and Charly Schwabe},
journal= {arXiv preprint arXiv:2512.01729},
year = {2025}
}