A categorical flop in dimension one
Algebraic Geometry
2026-03-24 v3
Abstract
In this note we observe that the categorical structure of a flop occurs for some well-known non-commutative resolutions of a nodal curve. We describe the flop-flop spherical twists, and give a geometric interpretation in terms of Landau--Ginzburg models. The resolutions are all weakly crepant but not strongly crepant, and we formulate an intermediate condition that distinguishes the smaller ones.
Cite
@article{arxiv.2505.06940,
title = {A categorical flop in dimension one},
author = {Calum Crossley},
journal= {arXiv preprint arXiv:2505.06940},
year = {2026}
}
Comments
v3: final version, incorporating referee suggestions