Classification of wormhole singularities
Algebraic Geometry
2025-12-10 v1 Combinatorics
Symplectic Geometry
Abstract
We classify all wormhole singularities, i.e. cyclic quotient surface singularities admitting at least two extremal P-resolutions, thereby solving an open problem posed by Urz\'ua. Our approach introduces a new combinatorial framework based on what we call the coherent graph of a framed triangulated polygon. As an application, we give an alternative proof of the Hacking-Tevelev-Urz\'ua theorem on the maximum number of extremal P-resolutions of a cyclic quotient singularity.
Cite
@article{arxiv.2512.08189,
title = {Classification of wormhole singularities},
author = {Jaime Negrete},
journal= {arXiv preprint arXiv:2512.08189},
year = {2025}
}