The Deligne-Simpson problem via 2-Calabi-Yau categories
Algebraic Geometry
2026-04-14 v2 Representation Theory
Abstract
We provide a short proof of the necessity of Crawley-Boevey's condition in his solution to the Deligne-Simpson problem. The proof relies on the local neighbourhood theorem for -Calabi-Yau categories due to Davison together with Crawley-Boevey's sufficient condition for the existence of local systems with prescribed conjugacy classes of monodromy around the punctures.
Keywords
Cite
@article{arxiv.2604.06991,
title = {The Deligne-Simpson problem via 2-Calabi-Yau categories},
author = {Lucien Hennecart},
journal= {arXiv preprint arXiv:2604.06991},
year = {2026}
}
Comments
There is a mistake in the way Theorem 3.3 is formulated, leading to a gap in the proof, as it currently assumes implicitly connectedness of some moduli spaces